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Volume II 



































artists’ materials 


































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V O L U M E I I 


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STUDY OF A DRAGON to face page 1 8 

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M.S, Codice Atlantico 9 r. 


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Institut de France^ MS. C 1 9 r. 


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Bibliotheque Nationale^ MS. 2037 4 r. 


BibliotMque Nationale., MS. 2037 5 v. 

allegory: MAIDEN WITH UNICORN 473 

British Museum 

allegory: combat of animals 473 



PROGRESS TO SUPREME POWER (See Colvin: Oxford Drawings) 490 
Library of Christ Church, Oxford 

ALLEGORY OF CONCORDAT (December 1515) between FRANCIS I 

AND LEO X (See Popp: Leonardo Zeichnungen) 492 

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MS. Codice Atlantico 145 <17. 


MS. Codice Atlantico 395 r. a 

ACADEMIA LEONARDi vTci (Print after Leonardo) 588 

British Museum 



The Nature of Water 

'As from the said pool of blood proceed the 
veins which spread their branches through the 
human body, in just the same manner the ocean 
fills the body of the earth with an infinite 
number of veins of water.’ 

If a drop of water falls into the sea when this is calm, it must of 
necessity be that the whole surface of the sea is raised imperceptibly, 
seeing that water cannot be compressed within itself like air. 

c,A. 20 r. a 

Whether the surface of the air is bounded by the fire, as is the water 
by the air and the earth by the water, and whether the surface of the 
air takes waves and eddies as does the surface of the water, and whether 
in proportion as the body of the air is thinner than that of the water the 
revolutions of its eddies are greater in number: of the eddies of the 
water some have their centres filled with air, others with water. I do not 
know whether it is the same with the eddies of the surface of the fire. 
Of the eddies of the water all those which begin at the surface are filled 
with air, and those that have their origin within the water are filled with 
water; and these are more lasting because water within water has no 
weight as water has when it is above the air; therefore the eddies of the 
water round the air have weight and speedily perish. c a 42 r a 


The deluges of rivers are created when the mouths of the valleys 
cannot afford egress to the waters that they receive from these valleys as 
rapidly as the valleys receive them. 

The progress of the water is swifter when it falls at a greater angle. 


The wave is the recoil of the stroke, and it will be greater or less in 
proportion as the stroke itself is greater or less. A wave is never found 
alone, but is mingled with as many other waves as there are uneven 
places in the object where the said wave is produced. At one and the 
same time there will be moving over the greatest wave of a sea innumer- 
able other waves proceeding in different directions. If you throw a stone 
into a sea with various shores, all the waves which strike against these 
shores are thrown back towards where the stone has struck, and on meet- 
ing others advancing they never interrupt each other’s course. Waves 
of equal volume, velocity and power, when they encounter each other 
in opposing motion, recoil at right angles, the one from the stroke of 
the other. That wave will be of greater elevation which is created by the 


greater stroke, and the same is true of the converse. The wave produced 
in small tracts of water will go and return many times from the spot 
which has been struck. The wave goes and returns so many more times 
in proportion as the sea which produces it contains a less quantity of 
water, and so conversely. Only in the high seas do the waves advance 
without ever turning in recoil. In lesser tracts of water the same stroke 
gives birth to many motions of advance and recoil. The greatest wave 
is covered with innumerable other waves moving in different directions; 
and these have a greater or less depth as they are occasioned by a greater 
or less power. The greatest wave is covered with various waves, which 
move in as many different directions as there were different places from 
which they separated themselves. The same wave produced within a 
small tract of water has a greater number of other waves proceeding 
over itself, in proportion to the greater strength of its stroke and recoil 
from the opposite shores. Greater is the motion of the wave than that 
of the water of which it is composed. Many waves turned in different 
directions can be created between the surface and the bottom of the 
same body of water at the same time. The eddying movements can 
accompany the direct movements of each wave. All the impressions 
caused by things striking upon the water can penetrate one another 
without being destroyed. One wave never penetrates another; but they 
only recoil from the spot where they strike. ^ 

The movement of water within water proceeds like that of air 
within air. ^ io8 v. a 

Among irremediable and destructive terrors the inundations caused 
by rivers in flood should certainly be set before every other dreadful and 
terrifying movement, nor is it, as some have thought, surpassed by 
destruction by fire. I find it to be the contrary, for fire consumes that 
which feeds it and is itself consumed with its food. The movement of 
water which is created by the slopes of the valleys does not end and die 
until it has reached the lowest level of the valley; but fire is caused by 
what feeds it, and the movement of water by its wish to descend. 
The food of the fire is disunited, and the mischief caused by it is dis- 
united and separated, and the fire dies when it lacks food. The slope of 
the valley is continuous and the mischief done by the destructive 
course of the river will be continuous until, attended by its valleys, it 



ends in the sea, the universal base and only resting place of the 
wandering waters of the rivers. 

But in what terms am I to describe the abominable and awful evils 
against which no human resource avails? Which lay waste the high 
mountains with their swelling and exulting waves, cast down the 
strongest banks, tear up the deep-rooted trees, and with ravening 
waves laden with mud from crossing the ploughed fields carry with 
them the unendurable labours of the wretched weary tillers of the soil, 
leaving the valleys bare and mean by reason of the poverty which is 
left there. 

Among irremediable and destructive terrors the inundations caused 
by impetuous rivers ought to be set before every other awful and terrify- 
ing source of injury. But in what tongue or with what words am I to 
express or describe the awful ruin, the inconceivable and pitiless havoc, 
wrought by the deluges of ravening rivers, against which no human 
resource can avail? _ , 

Prove and draw up the rule for the difference that there is between 
a blow given by water upon water, and by water falling upon something 
hard; and consider well also that as water falls upon other water, and it 
yields space to the blow, the percussion making the water open as it 
receives the blow, so the same result will occur in a vase when the water 
which is contained within it has been struck, for it will be the same as 
when falling water has struck against a hard substance which resists 
the blow. j 

C.A. 153 V. d 


Among straight rivers which occur in land of the same character, 
with the same abundance of water and with equal breadth, length, 
depth, and declivity of course, that will be the slower which is the 
more ancient. 

This may be proved with straight rivers. That will be most winding 
which is the oldest, and that which winds will become slower as it 
acquires greater length. 

Of waters which descend from equal altitudes to equal depths that 
will be the slower which moves by the longer way. 

Of rivers which are at their commencement that will be the slower 
which is the more ancient, and this arises from the fact that the course is 



continually acquiring length by reason of the additional meanderings of 
the river; and the reason of this is explained in the twelfth section. 

c.A. 156 r. a 

The cause which moves the humours in all kinds of living bodies 
contrary to the natural law of their gravity, is really that which moves 
the water pent up within them through the veins of the earth and 
distributes it through narrow passages; and as the blood that is low 
rises up high and streams through the severed veins of the forehead, or 
as from the lower part of the vine the water rises up to where its branch 
has been lopped, so out of the lowest depths of the sea the water rises to 
the summits of the mountains, and finding there the veins burst open it 
falls through them and returns to the sea below. Thus within and 
without it goes, ever changing, now rising with fortuitous movement 
and now descending in natural liberty. 

So united together it goes ranging about in continual revolution. 

Rushing now here now there, up and down, never resting at all in 
quiet either in its course or in its own nature, it has nothing of its own 
but seizes hold on everything, assuming as many different natures as 
the places are different through which it passes, acting just as the mirror 
does when it assumes within itself as many images as are the objects 
which pass before it. So it is in a state of continual change, sometimes 
of position and sometimes of colour, now enclosing in itself new scents 
and savours, now keeping new essences or qualities, showing itself now 
deadly now lifegiving, at one time dispersing itself through the air, at 
another suffering itself to be sucked up by the heat, and now arriving 
at the region of cold where the heat that was its guide is restricted by it. 

And as when the hand under water squeezes a sponge so that the 
water that escapes from it creates a wave that passes through the other 
water, even so does the air that was mingled with the water when the 
cold^ is squeezed out, flee away in fury and drive out the other air; this 
then is the course of the wind. 

And as the hand which squeezes the sponge under water when it is 
well soaked, so that the water pent up within it is compelled to flee away 
and therefore is driven by force through the other water and penetrates 
it, and this second mass perceiving itself to be struck departs in a wave 
from its position, even so the new . . . makes . . . c.a. 17 i r. a 

^ quella del freddo. 



The sharp bends made in the embankments of rivers are destroyed 
in the great floods of the rivers because the maximum current drives the 
water in a straight course. But as this diminishes it resumes its winding 
course, during which it is being continually diverted from one bank to 
another, and as it thus grows less the embankment of the river becomes 
hollowed out. 

But in this lesser depth the water does not move with uniform course, 
because the greater current leaps from one hollow to another of the 
opposite banks, and the sides of the water which border upon the i 

embankment have the shortest course. I 

; The rotundities in the islands of shingle formed by the angles of the i 

embankment trace their origin to the chief eddies of the rivers, which 
extend with their revolutions among the concavities and convexities i 

which are found alternately in the embankments of the rivers; and ; 

, . from these spring the tiny brooks, interposed between the sandbanks 

of the rivers and their embankments, and placed opposite to the hollows 
' of the embankments of these rivers. 

The entry of river into river produces the first meanderings of the 
I ' river. 

The meanderings of rivers in plains are occasioned by the rivers 
emptying themselves there. 

If the winding river be altogether removed from its ancient bed and 
set in a straight channel, it is necessary that the rivers which pour 
themselves into it from two sides increase in length on the one side as 
much as they lose it on the other, the one that acquires length losing in 
swiftness, this swiftness being transferred to the one that grows shorter. 

Cause the lesser rivers to enter into the greater rivers at acute angles; 
the advantage of this will be that the current of the greater river diverts 
the line of entry of the lesser river and does not suffer it to strike against 
the opposite bank. I 

, Should however the lesser river be in flood at the time when the I 

? waters of the greater river are low the percussion of the lesser river will i 

\ ' break the opposite bank of this greater river. 

X The largest of the curves of a river in a valley will always have its 

convex side facing the lower part of the breadth of the valley. 

; The meanderings of rivers are always greater in proportion as they | 

, are nearer to the spot where the lesser river enters the greater. i 

The waves of earth formed by the embankment of the rivers are 

.15 i; 


continually changing their positions, the former being created anew 
where the latter have been washed away. ^ ^ 185 r. b 

Prove whether a triangle thrown into still water makes its wave of 
perfect roundness in the end. c.a. 199V. b 

\Sketch ^figure of bubble resting on water] 

Why the bubbles which the water makes are half-spheres and those 
of the air are perfect spheres. Why the sides of the base of the half- 
sphere are spherical rectangles, and the contact which each has with the 
water does not cause it to form a projection above it but on account of 
its weight it has to bend and curve. ^ ^ ^ ^ 

\Wtth drawing] 

The water that falls down from a height, will create a deep pool, 
which will continually increase, and its banks will often fall in. And the 
reason of this is that the water, which falls upon the other water, by the 
swiftness of its blow and by its weight causes it to give place, and passes 
down to its depths where it forms a hollow space, and through the stroke 
and the air, which as it falls is buried with it, it comes to rise up again and 
raise itself to a height by various channels, which expand like an opening 
bud, and the stroke of the water upon the bank proceeds in a circle and 
thus continuing it will gnaw and consume the surrounding shores. 

C.A. 215 V. d 

The air by its nature does not flee away beneath the water; but the 
water which is supported round about it presses it out of itself and drives 
it forth. 

Therefore one element does not flee away of itself out of the other 
element, but is driven out by it. 

, C.A. 244 V. a 


The flow and ebb of the sea are due to the course of the rivers, which 
give the water back again to the sea with slower movement than the 
movement of their own current; and on this account necessity causes 
the water to rise to a height. And this river covers up its current again 
with the swift wave which in its recoil goes to meet the descending 
current of the river. 

. ; 16 ■ 


The wave of the river flows back against its current when the sea 
is at its ebb. After the return of the wave to the shore it there acquires 
new power from the approach of the river. 

The flow and ebb of the sea are not caused by the moon or the sun, 
but by the greatest wave as it advances and falls back. But since the 
recoil is weaker than the advancing movement, as it is deprived of 
support, this hesitating movement would consume itself if it were not 
renewed by the help of the rivers; for these being immediately swollen 
by the approaching wave of the aforesaid tide, the wave produced by 
this swollen river becomes added to this ebb, and it strikes the opposite 
shores of the islands set over against it, and then leaps back, and so 
returns in its former course, and so continues, as has been said above. 

This experience has taught us, for it is seen continually in every 
river, and especially as it strikes against the sides of its bays, 

C.A. 281 r. a 

The spiral or rotary movement of every liquid is so much the swifter 
in proportion as it is nearer to the centre of its revolution. 

This that we set forth is a circumstance worthy of note; since move- 
ment in the circular wheel is so much slower as it is nearer to the centre 

of the revolving object. But this same circumstance is shown in the 
similarity of movement both as to speed and length in each complete 
revolution of the water, both in the circumference of its greater and of 
its lesser circle; but the curve of the lesser circle is as much less than that 
of the greater as the greater circle is more curved than the lesser. And 
so this water is of uniform movement in all the processes of its revolution, 
and if it were not so the concavity would instantly be filled up again. 
But because the lateral weight of this eddying mass" is twofold, such 
concavity has no permanent movement, and of such duplication of 
weight the first comes into being in the revolving movement of the water, 
the second is created in the sides of this concavity, and it supports itself 
there and finally falls headlong down upon the air which has filled up 
the aforesaid cavity with itself. 

The movements of the air through the air are two, that is straight in 
the form of a column upwards, and with revolving movement. 

But water makes this movement downwards, and makes it in the form 
of a pyramid, and makes it so much the more swiftly as the pyramid is 
more pointed. c.a. 296 V. b 

^ yi.%. circulazion reverti^nosa. 

B 2 ■ 17 



There were many of the chief towns of the districts which, through 
being placed upon their chief rivers, have been consumed and destroyed 
by these rivers, as was Babylon by the Tigris, by means of Cyrus . . . and 
so with an infinite number of regions ; and the science of water gives 
exact information as to their defences. ^ ^ 

Water falling perpendicularly into running water makes a curve as 
it enters and a curve as it rises. The summit of the part that rises in the 
air will not be in the centre of the base of this cavity, and this base will be 

c,., 343 V. a 


The water falls in whatever is the line of the summit of its wave, and 
it moves more swiftly where this fall has less slant, and breaks more into 
foam where it meets with more resistance. 

There, according to what has been stated, the waves break against 
the course of the river and never in the direction of its course, because 
water falling upon flowing water can never create a rebound upon 
something that flies away and does not await the stroke; but in the case of 
the opposite descent towards the course of the water, the water in the 
wave as it falls against the course of the river does not come upon water 
which flies away from its stroke, but upon water which is proceeding 
in the opposite direction to this fall; and consequently as the wave in its 
fall has four degrees of velocity and the water that comes to meet it is 
also of four degrees of velocity, the impetus of the wave acquires eight 
degrees of velocity, and therefore waves of rivers break against their 
current, and that of the sea breaks against the water that flies back from 
the shore against which it has struck, and not against the wind that 
drives it. , 

C.A. 354 r. b 


Every movement of water creates flow and ebb in every part of the 
river where the swiftness of its course checks it. 

This is proved by the fact that where the course of the river is 
steeper it is swifter; and where it is more level it is slower. Therefore the 
level sea receives more water than it discharges; for which reason it is 
necessary for the water of the sea to rise to such a height that its weight 


Royal Library^ Windsor 

the nature of water 

overcomes the water that drives it; and then this water which has been 
driven descends from its height round about the base of the aforesaid 
hill, and that part which descends against the current mentioned before 
swells this current up in such a way that the upper part of its water is 
retarded, until the water that follows becoming more abundant subdues 
the ebb and creates a new flow. 

C.A. 354 r. e 

The impetus made in the great current of the water preserves its 
line among the motionless waves as the solar ray may do in the course of 
the winds. 

At one time the wave of the impetus is motionless amid the great 
current of the water, at another it is extremely swift in the motionless 
water, that is on the surface of the swamps. 

Why does a blow upon the water create many waves? 

C.A. 354 V. a 

The river which has always depth at the centre of its course will 
keep within its banks. 

Where the channel is more confined, there the water runs more 
strongly than elsewhere, and as it issues from the straight it spreads 
itself furiously, and strikes and wears away the near banks which lie 
across its course, and often changes its course from one place to another. 

C.A. 361 r. b 

The movement of the wind resembles that of the water. 

What is the difference between water which is drawn and water 
which is driven? 

Water which is drawn is when the Ocean as it falls draws after it the 
water of the Mediterranean Sea. 

Water driven is that caused by the rivers which, as they come into the 
sea, drive its water. 

Amid all the causes of the destruction of human property, it seems 
to me that rivers on account of their excessive and violent inundations 
hold the foremost place. And if as against the fury of impetuous rivers 
any one should wish to uphold fire, such a one would seem to me to be 
lacking in judgment, for fire remains spent and dead when fuel fails it, 
but against the irreparable inundation caused by swollen and proud 
rivers no resource of human foresight can avail; for in a succession of 
raging and seething [waves], gnawing and tearing away the high banks, 

■ .19 ■ 


growing turbid with the earth from the ploughed fields, destroying the 
houses therein and uprooting the tall trees, it carries these as its prey down 
to the sea which is its lair, bearing along with it men, trees, animals, 
houses and lands, sweeping away every dike and every kind of barrier, 
bearing with it the light things, and devastating and destroying those of 
weight, creating big landslips out of small fissures, filling up with its 
floods the low valleys, and rushing headlong with insistent and inexor- 
able mass of waters. 

What a need there is of flight for whoso is near! O how many cities, 
how many lands, castles, villas and houses has it consumed! 

How many of the labours of wretched husbandmen have been 
rendered idle and profitless! How many families has it brought to 
naught, and overwhelmed ! What shall I say of the herds of cattle which 
have been drowned and lost! 

And often issuing forth from its ancient rocky beds it washes over 
the tilled riandsl ... 

L J c.A. 36iv. a 

Where the channel of the river is more sloping the water has a 
swifter current; and where the water is swifter it wears the bed of its 
river more away and deepens it more and causes the same quantity of 
water to occupy less space. 

The shorter the course of the rivers the greater will be their speed. 
And so also conversely it will be slower in proportion as their course has 
greater length. 

Where the superabundance of the water is not received within the 
depth ofits channel, necessity causesit to fall precipitately outsideits banks. 

No part of an element possesses weight within its element unless it is 
either moved within it with impetus, or falls down within it, being drawn 
by it from within another element. , 

c.A. 365 r. a 

The course of a smaller flood of water conforms to that of the 
larger of the great floods, and changes course and keeps company with 
it and ceases to delve under the banks. 

The proof of this is seen in the Po. For when it is low its water runs 
many times in cross-currents, and called by the low places and directing 
its way towards these it takes its course and strikes the bank in its 
foundations, and hollows these out causing wide destruction. But when 
it flows in full stream the lesser quantity which formerly with its cross- 


current had beaten upon the banks and hollowed them, abandons its 
course, being dragged in company with the greater volume of water and 
advancing along the line of its base it forbears to damage its banks. 

A 23 V. 

The water which falls by the line nearest to the vertical is that which 
descends most rapidly and gives itself with greatest blow and greatest 
weight to the spot on which it strikes. 

. Every stream of water when near to its fall will have the curve of the 
descent commencing on the surface before it commences in the depth. 

A 24 r. ■: 

Water is by its weight the second element that encompasses the earth, 
and that part of it which is outside its sphere will seek with rapidity to 
return there. And the farther it is raised above the position of its element 
the greater the speed with which it will descend to it. Its qualities are 
dampness and cold. It is its nature to search always for the low-lying 
places when without restraint. Readily it rises up in steam and mist, and 
changed into cloud falls back again in rain as the minute parts of the 
cloud attach themselves together and form drops. And at different 
altitudes it assumes different forms, namely water or snow or hail. 
Constantly it is buffeted by the movement of the air, and it attaches itself 
to that body on which the cold has most effect, and it takes with ease 
odours and flavours. ■ , ^ 

It is not possible that dead water should be the cause of movement 
either of itself or of anything else. ^ _ 


Man has been called by the ancients a lesser world, and indeed the 
term is rightly applied, seeing that if man is compounded of earth, 
water, air and fire, this body of the earth is the same; and as man has 
within himself bones as a stay and framework for the flesh, so the world 
has the rocks which are the supports of the earth; as man has within him 
a pool of blood wherein the lungs as he breathes expand and contract, 
so the body of the earth has its ocean, which also rises and falls every six 
hours with the breathing of the world; as from the said pool of blood 
proceed the veins which spread their branches through the human 
body, in just the same manner the ocean fills the body of the earth 


with an infinite number of veins of water. In this body of the earth 
there is lacking, however, the sinews, and these are absent because 
sinews are created for the purpose of movement, and as the world is 
perpetually stable within itself no movement ever takes place there, and 
in the absence of any movement the sinews are not necessary; but in 
all other things man and the world show a great resemblance. 


Clearly it would seem that the whole surface of the ocean when not 
affected by tempest is equally distant from the centre of the earth, and 
that the tops of the mountains are as much farther removed from this 
centre as they rise above the surface of the sea. Unless therefore the 
body of the earth resembled that of man it would not be possible that 
the water of the sea being so much lower than the mountains should have 
power in its nature to rise to the summit of the mountains. We must 
needs therefore believe that the same cause that keeps the blood at the 
top of a man’s head keeps water at the summit of mountains. 


Where there is life there is heat, and where there is vital heat there is 
movement of vapour. This is proved because one sees that the heat of 
the element of fire always draws to itself the damp vapours, the thick 
mists and dense clouds, which are given off by the seas and other lakes 
and rivers and marshy valleys. And drawing these little by little up to 
the cold region, there the first part halts, because the warm arid moist 
cannot exist with cold and dryness; and this first part having halted 
receives the other parts, and so all the parts joining together one to 
another form thick and dark clouds. 

And these are often swept away and carried by the winds from one 
region to another, until at last their density gives them such weight that 
they fall in thick rain; but, if the heat of the sun is added to the power of 
the element of fire, the clouds are drawn up higher and come to more 
intense cold, and there become frozen and so produce hailstorms. 

So the same heat which holds up so great a weight of water as is seen 
to fall in rain from the clouds sucks it up from below from the roots of the 
mountains and draws it up and confines it among the mountain summits, 



and there the water finds crevices, and so continuing it issues forth and 
creates rivers. a 54 V. 

If heat is the cause of the movement of moisture cold stops it. This 
has been already shown by the example of the cold region which stops 
the clouds drawn by the hot element. As for the proof that the heat 
draws the moisture it is shown as follows: —heat ajug and set it in a vase 
with the mouth downwards, and place there some charcoal which has 
been lighted. You will see that the moisture as it retires before the heat 
will rise and fill the jug with water, and the air which was enclosed in 
this jug will escape through its opening. 

Also if you take a wet cloth and hold it to the fire you will see the 
damp of the cloth leave its place, and that part of the moisture which has 
least substance will rise up, drawn by the proximity of the fire which 
from its nature rises towards the region of its element. In this way the 
sun draws up the moisture. 


I say that it is just like the blood which the natural heat keeps in the 
veins at the top of the man, and when the man has died this blood 
becomes cold and is brought back into the low parts, and as the sun 
warms the man’s head the amount of blood there increases, and it 
grows to such an excess there with the humours as to overload the veins 
and frequently to cause pains in the head. It is the same with the springs 
which ramify through the body of the earth and, by the natural heat 
which is spread through all the body that contains them, the water stays 
in the springs and is raised to the high summits of the mountains. And 
the water that passes through a pent-up channel within the body of the 
mountain like a dead thing will not emerge from its first low state, 
because it is not warmed by the vital heat of the first spring. Moreover 
the warmth of the element of fire, and by day the heat of the sun, have 
power to stir up the dampness of the low places and draw this to a height 
in the same way as it draws the clouds and calls up their moisture from 
the expanses of the sea. a 561. 

Of the opinion held by some that the water of some seas is higher 
than the highest summits of the mountains and that the water was 
driven up to these summits; 


Water will not move from one spot to another unless to seek a lower 
level, and in the natural course of its current it will never be able to 
return to an elevation equal to that of the spot whence it first issued forth 
from the mountains and came into the light. That part of the sea which 
by an error of imagination you state to have been so high as to have 
flowed over the summits of the high mountains for so many centuries, 
would be consumed and poured out in the water that has issued from 
these same mountains. You can well imagine that during all the 
time that the Tigris and the Euphrates have flowed from the summits 
of the Armenian mountains, ^ one may suppose the whole of the 
water of the ocean to have passed a great many times through their 

Or do you not believe that the Nile has discharged more water into 
the sea than is at present contained in all the watery element? Surely 
this is the case. If then this water had fallen away from the body of the 
earth, the whole mechanism would long since have been without water. 
So therefore, one may conclude that the water passes from the rivers to 
the sea, and from the sea to the rivers, ever making the self-same round, 
and that all the sea and the rivers have passed through the mouth of the 
Nile an infinite number of times. .x j 


Water which falls from a height into other water imprisons within 
itself a certain quantity of air, and this through the force of the blow 
becomes submerged with it. Then with swift movement it rises up 
again and arrives at the surface which it has quitted, clothed with a fine 
veil of moisture spherical in form, and proceeds by circles away from the 
spot where it first struck. Or the water which falls down upon other 
water runs away from the spot where it strikes, in various diiferent 
branches, bifurcating and mingling and interlacing one with another; 
and some, being hollow, are dashed back upon the surface of the water; 
and so great is the force of the weight, and of the shock caused by this 
water, that through its extreme swiftness the air is unable to escape into 
its own element, but on the contrary is submerged in the manner that 
I have stated above. 

^ Text is not de monti eruini, as given in M. Ravaisson-Mollien’s transcript, but 
mhti ermjnj {de monti emwi), as given by Dr, Richter. 



V A R I O U S P L A C E S 

The movement of water tends always to wear away its support;. and 
the part which is the softest offers the least resistance, and as it vacates 
its place it leaves various hollows in which the water, whirling round in 
divers eddies, wears away and hollows out and increases these chasms, 
and striking against the newly-bared dikes leaps back and strikes upon 
the banks, consuming and eating away and destroying whatever stands 
in its path, changing its course in the midst of the havoc it has made, 
dragging with it in its course the lightest of the soil and then depositing 
it in the parts that are more tranquil. As it raises its bed the quantity 
and force of the water is lessened and its fury is transferred to the opposite 
side, and when it reaches the bank it eats it away and lays its foundations 
bare until with great destruction it has uncovered new ground. If it 
should find a plain it covers it, and carrying away and hollowing out it 
forms a new bed, and if it should come upon buried stones it uncovers 
them and lays them bare. But it often happens that these, because of 
their size, make resistance to the impetuous flood, and so after being 
driven against the rocks that are in the middle of its course it leaps back 
towards the opposite side, breaking and destroying the opposite bank. 

A 59 r. 


Water which falls in the manner stated does not enlarge its pit, for 
as the fact of it falling perpendicularly shows, there is but little force in 
the water that drives it from behind, and this is why it falls all broken 
and in fine spray almost in a perpendicular line. And the air which is 
amidst this broken water having an almost equal weight above it cannot 
escape so quickly as not to be submerged by the weight together with 
the blow. But, since air cannot be disunited from its element without 
violence, after yielding to the fury of the blow and the weight, it rises 
again quickly and returns to the surface in round bubbles near to the 
spot that was struck, and so as it does not move any distance from this 
spot it does not cause any damage to the banks of the pit. But when the 
rushing river, swollen by recent rains, scours its banks, it falls in fury into 
the lower waters, and no longer as formerly descending peacefully in a 
shower mingled with air upon the other water but united and strong, 


strikes and tears open the smitten depths right down to their rocky bed, 
uncovering and carrying awa^ the buried stones, setting up for itself a 
new barrier in the shingle carried from the pit which it has made it 
throws itself upon it and falls back beaten, and divides at the blow into 
two different streams which separate and form half-circles, devouring and 
consuming every obstacle and enlarging their bed in the form of a circle. 

To put it more exactly — when the rivers are in flood, the falls of 
the water are less abrupt, and therefore, as the mass of water strikes the 
lower levels, the water which follows the blow does not hasten with the 
violence of that which falls, and this being the case it offers resistance 
and thus offering resistance the water rises and the fall becomes shorter. 
In consequence it does not imprison so much air, because the lower parts 
of the water are hardly separated from the rest in its fall and, owing to 
this, very little air can enter, and therefore the blow and weight of the 
water meet with no resistance, and the blow proceeds without diminish- 
ment right down to the bottom, displacing the gravel that is there and 
surrounding and clothing the stones with itself and increasing the depth 
of the pools. A 59 r. and v. 


The reason is that in the beds of rivers there are always found stones 
of different sizes, and as the water, coming to the largest, sinks down be- 
hind them and smites the spot on which it falls, the blow dislodges the 
lesser stones from the spot on which it strikes, and the bed is made 
larger. As the fall increases it becomes more powerful and hollows out 
even more the pit which has been begun; and this occurs because the 
rivers constantly gnaw the mud of their bed and constantly uncover and 
lay bare rocks of different forms and sizes. 


The reason of this is that just as a pair of stockings which cover the 
legs reveal what is hidden beneath them, so the part of the water which 
lies on the surface reveals the nature of its base, inasmuch as that part 
of the water which bathes its base, finding there certain protrusions 
caused by the stones, strikes upon them and leaps up raising with it all 
the other water which flows above it. a 59 v. 




The reason of this is that the water which strikes this rock afterwards 
descends and makes a kind of pit, in which in its course it searches for 
the hollow and then leaps back to a height and again falls down to the 
bottom and does the same, so continuing many times, like a ball that is 
thrown on the ground which before it finishes its course makes many 
bounds each smaller than the one before it. 

All the movements of the wind resemble those of the water. 
Universally all things desire to maintain themselves in their natural 
state. So moving water strives to maintain the course pursuant to the 
power which occasions it, and if it finds an obstacle in its path it com- 
pletes the span of the course it has commenced, by a circular and revolv- 
ing movement. 

So when water pours out of a narrow channel and descends with fury 
into the slow-moving currents of mighty seas — since in the greater bulk 
there is greater power, and greater power offers resistance to the lesser — 
in this case, the water descending upon the sea beats down upon its 
slow-moving mass, and this cannot make a place for it with sufficient 
speed because it is held up by the rest of the water; and so the water that 
descends, not being willing to slacken its course, turns round after it has 
struck, and continues its first movement in circling eddies, and so fulfils 
its desire down in the depth; for in these same eddies it finds nothing 
more than its own movement, which is attended by a succession of circles 
one within the other; and by thus revolving in circles its course becomes 
longer and more continuous, ’because it meets with no obstacle except 
itself; and this motion eats away and consumes the banks, and they fall 
headlong in ruin. ... a 6o r. 


The reason of this is that, if the circles which above are large become 
reduced to a point as they are submerged, and then continue their move- 
ment in the direction in which it began, the water will at the bottom 
make a movement contrary to that above when it separates itself from 
its centre. 


Although the sounds which traverse the air proceed from their 
sources by circular movements, nevertheless the circles which are pro- 
pelled by their different motive powers meet together without any 
hindrance and penetrate and pass across one another, keeping always 
their causes as their centres. 

Since, in all cases of movement, water has great conformity with air, I 
will offer it as an example of the above-mentioned proposition. I say 
that, if at the same time you throw two small stones into a large lake of 
still water at a certain distance one from another, you will observe two 
distinct sets of circles form round the two points where they have struck; 
and as these sets of circles grow larger they come to meet together and 
the circles intersect one with another, always keeping as their centres the 
spots which were struck by the stones. The reason of this is that although 
some show of movement may be visible there, the water does not depart 
from its place because the openings made there by the stones are 
instantly closed; and the movement occasioned by the sudden opening 
and closing of the water makes a certain shaking which one would 
define as a quivering rather than a movement. That what I say may be 
more evident to you, just consider those pieces of straw which on 
account of their lightness float on the surface of the water and are not 
moved from their position by the wave that rolls beneath them as the 
circles widen. This disturbance of the water, therefore, being a 
quivering rather than a movement, the circles cannot break one another 
as they meet, for, as all the parts of water are of a like substance, it 
follows that these parts transmit the quivering from one to another 
without changing their place, for, as the water remains in its position, 
it can easily take this quivering from the parts near to it and pass it on 
to other parts near to it, its force meanwhile steadily decreasing until 
the end. 

A 6i r. 

The winding courses of the water caused by the rebounds of the 
percussions which they make against the banks will cause the bed of the 
river below them to be more hollowed out than any other part; and in 
their percussions they will become of great depth; and the water that is 
whirled round near to these deep places will serve to undermine and 
destroy the banks against which it strikes. 

One both clearly sees and recognises that the waters which strike 
the banks of the rivers act in the same way as balls which, when they are 



struck against walls, rebound from these at angles similar to those at 
which they strike, and proceed to strike against the opposite sides of the 
walls. So these waters after having first struck against the one bank, leap 
back towards the opposite one and strike upon it and hollow it out with 
vigour, because there is a greater confluence of water in this spot. The 
reason of this is that the water which leaps back from one bank to another 
hollows out that part of the bed of the river which finds itself beneath it; 
and the other water of the river which cannot be received in this low 
part remains repulsed and thrown back somewhat by the direct course 
of the river. And having no way of escape, it returns to its natural course, 
that is, that, as the bed of the river finds itself lower under the winding 
ways made by the above-mentioned percussions of the waters, this 
second water, which has lost its adventitious means of escape, resumes its 
natural course, falls into the lower parts of the river and strikes the banks 
at the same spot as that which witnessed the percussion of the aforesaid 
rebounds. As this bank is thus assailed by two entirely different sets of 
percussions a larger hollow is caused in it, for, while the first strike 
the bank above, the others descending more steeply devour and lay it 
bare at its base, and this is the cause of the aforesaid destruction and 
subsidence of the banks. a 63 V 

o F w A T E R 

No part of the watery element will raise itself or make itself more 
distant from the common centre except by violence. No violence is lasting. 

c 15 r. 


This is because [confined] water when struck by a blow cannot make 
its impetus pass from circle to circle as it would in a great lake; and 
since the water when struck finds near to itself the edges of the bucket, 
which are harder and more resisting than the other water, it cannot 
expand itself, and consequently it comes about that the whole of its 
impetus is turned upwards; and therefore water struck by a stone 
throws its drops up higher when its waves are confined than when they 
have a wide space. c 221 

\Of the motion of water\ 

Water or anything falling upon water causes the water that receives 
the blow to spread itself out beneath the blow and to surround it, and 

, 29 ■ 


having passed over the cause of this blow it continues above it in pyra- 
midal shape and then falls back to the common level. 

The reason of this is that when a drop of water falls from a roof upon 
other water, the part that receives the blow cannot find room or escape 
within the rest of the water with the speed with which it has been 
attacked, because it would be necessary for it to support too much weight 
in order to enter under so great a quantity of water. Having therefore 
to obey its own course as well as the action of that which drives it from 
its place, and finding that as the adjacent water does not receive the 
blow and is not ready for a similar flight it cannot penetrate it, it seeks 
instead the shortest way and flows through the substance that offers it 
less resistance, namely the air. 

And as this first circle that surrounds the place which has been struck 
closes up with fury, because it was raised above the common surface of the 
water, it reduces the water that escapes upwards to the form of a pyramid. 

And if you think that the water which falls was the same as that which 
leaps up, make a small stone drop into the water and you will see the 
water leap up in the same way and not the stone. 

-T J C 22 V. 

Every part of water within other water that is without movement lies 
equally at rest with that situated at the same level. 

Here experience shows that if there were a lake of very great size 
which lay without movement of wind either entering or departing, and 
if you were to remove a very small part of the height of the bank which 
is IdcIow the surface of the water, all the water that is above the top of the 
bank that was cut away will pass through this cutting, but will not set in 
movement or draw with it out of the lake any part of the water that lay 
there before this water moved and went away. 

In this instance nature is constrained by the workings of its law 
which lives infused within it, namely, that all the parts of that surface of 
the waters which are supported by the banks without any opening or exit 
are situated at an equal distance from the centre of the earth. 

^ c 23 V. 

R O L L E D O V E R B Y W A T E R 

Know that stones are rolled over by water because this water either 
surrounds or flows over them. If it surrounds them it meets again be- 
yond them and intersects, hollowing out the soil or sand beyond the 

■ 30 


stone, and this after being thus laid bare begins to roll of itself. And if 
the water flows over the stone, then after it has done so it falls in the same 
line, and by the force of its impetus penetrates from the surface to the 
base of the other water, and gnaws and tugs and drags away the stone 
from the opposing obstacles with the result that this also begins to roll, 
and so continues from place to place until it traverses the whole river. 
And if a lesser stone should stand in its path the water uncovers it by the 
same process and does the same, and in this way stones are rolled over 
in the beds of flowing rivers. c 24 v 

A horse or man or any other creature that makes its way through 
stagnant water of medium depth will cause this water to rise and cover 
a quantity of the shore towards which this creature is directing its course. 

This may be clearly demonstrated ; for if you take a step in this water 
you will find that it makes a wave which directs its course and moves 
in the same direction as that in which the creature is travelling; nor does 
it pause until it has achieved its desire and covered a small part of the 

A second step creates another wave which has a similar result, and 
the same with the third and all the steps; each of itself creating a wave 
that travels as far as the shore, in such a way that this shore which 
formerly was uncovered finds itself covered by water over a great dis- 
tance — then when you have emerged from this water you will see it 
returning to its former position in swift course. ^ ^ 

Waves of rivers that flow against the courses of the winds will be of 
greater height than others. 

The rivers that move against the courses of the winds will have a 
greater current below than above, as their surface on being driven by 
the winds becomes slower than it was at first. 

The reason of this is that if the rivers, being of equal depth and 
breadth, are of uniform current at the bottom and on the surface, the 
resistance made by the wind to the current on the surface must neces- 
sarily cause it to turn back, and as it does not suffice these waves to raise 
themselves a little, falling at last they enter underneath the others and 
proceed to the bottom. Finding there the other current of the bottom 
it accompanies it, and as the bank is not capable of containing this 
increase it is necessary that at the bottom the current doubles itself; if it 

were not so one would see the water rising far above the banks of the 
rivers. ^^5^. 

The stone placed in the level and smooth beds of flowing rivers 
becomes the cause of their inequality and deterioration. 

When an object which is dropping down strikes upon another object 
harder than itself it suddenly makes a rebound which is so much greater 
as it has had a greater fall. When therefore a stone is situated beneath 
the surface of running rivers, the greater its size the greater is the per- 
cussion that takes place when water falls from its summit upon the beds 
of the rivers, and on account of this it comes to produce a deeper hollow 
in the place struck by this water. 

After this first percussion many rebounds will follow, and these will 
become larger in size and less powerful as they are farther removed from 
the first. 

The embankment which sends forth the trunk of the tree that it has 
nourished, to project into the waves of the rapid rivers, will become the 
cause of the destruction of the opposite bank. 

The cause of this effect is that the water that flows in the rivers 
always goes leaping from bank to bank. If nothing projects in this bank 
many lines of water gather there and unite together and leap in a mass 
on the opposite bank, and twist themselves in with the other lines 
which they meet with on their way; and having reached the embank- 
ment they gnaw and destroy it. And there are yet new lines produced 
there which leap back and damage the other bank; and so from place to 
place they begin to form eddies of varying depths, and hence it comes 
about that straight rivers become winding and crooked. ^ ^ 

W H A T W A T E R I S 

Of the four elements water is the second least heavy and the second 
in respect of mobility. It is never at rest until it unites with its maritime 
element, where, when not disturbed by the winds, it establishes itself 
and remains with its surface equidistant from the centre of the world. 
It is the increase and humour of all vital bodies. Without it nothing 
retains its first form. It unites and augments bodies by its increase. 

Nothing lighter than itself can penetrate it without violence. 

It readily raises itself by heat in thin vapour through the air. Cold 

-32. ■ ; ■ . , 


causes it to freeze. Stagnation make it foul. That is, heat sets it in 
movement, cold causes it to freeze, immobility corrupts it. 

It assumes every odour, colour and flavour, and of itself it has 
nothing. It percolates through all porous bodies. Against its fury no 
human defence avails, or if it should avail it is not for long. In its rapid 
course it often serves as a support to things heavier than itself. It can lift 
itself up by movement or bound as far as it sinks down. It submerges 
with itself in headlong course things lighter than itself. The mastery 
of its course is sometimes on the surface, sometimes in the centre, 
sometimes at the bottom. One portion rises over the transverse course 
of another, and but for this the surfaces of the running waters would be 
without undulations. Every small obstacle whether on its bank or in its 
bed will be the cause of the falling away of the bank or bed opposite 
to it. When the water is low it does more damage to the bank in its 
course than it does when it flows in full stream. Its parts do not weigh 
upon the parts placed beneath them. No river will ever keep its course 
in the same direction between its banks. Its upper parts do not impart 
weight to the lower. 

\An expermeni\ 

I wish to show you in what manner water can be supported by air 
while being divided and separated from it. Certainly if you have reason 
in you, I believe that you will not deny that if there be a leather bag 
placed at the bottom of the water in a well, so as to touch all its sides, 
in such a way that the water cannot pass beneath, if this leather bag be 
filled with air it will not exert less force in rising to the surface of the 
water to find the other air than the water makes in its desire to touch the 
bottom of the well. And if this leather bag desires to rise up it will push 
up the water that is placed above it, and by raising this water it will take 
its weight from off the bottom of the well. For this reason therefore it is 
almost as though the well were bottomless. 

Where and why the movement of the water ought to hollow out the 
sand of the surface of the beds of flowing rivers — but to speak first of 
the percussion on the surface: 

The more rapid the current of the water along the slope of a smooth 
canal the more powerful will be its percussion against whatever opposes it, 

■ 33 ' ■ . 


For all the elements when removed from their natural position desire 
to return to it, especially fire, water and earth; and the shorter the line 
along which this return is made, the straighter its course, and the 
straighter its course the greater the percussion upon whatever opposes it. 

The same effect is produced by the wind blowing through streets 
of uniform widths ^ 26 v. 


Define first of all what is height and depth, also how the elements are 
situated one within the other. Then what is solid weight and liquid 
weight; but first of all what weight and lightness consist of in themselves. 
Then describe why water moves, and why its motion ceases; then why it 
becomes slower or more rapid, and in addition to this how it continually 
descends when in contact with air that is lower than itself; and how the 
water rises in the air through the heat of the sun and then falls back in 
rain. Further, why the water springs from the summits of the mountains, 
and whether any spring of water higher than the ocean can pour forth 
water higher than the surface of this ocean; and how all the water that 
returns to the ocean is higher than the sphere of the water: and how the 
water of the equinoctial seas is higher than the northern waters, and is 
higher beneath the body of the sun than in any other part of the circle 
of the equator; for when the experiment is made under the heat of a 
burning brand, the water boils as the effect of the brand, and the water 
around the centre of where it boils descends in a circular wave. And how 
the waters of the north are lower than the other seas, and more so as they 
become colder, until they are changed into ice, e 1 2 r 


That river which stretches itself out most by long tortuous windings 
is the one which becomes filled up most rapidly with matter. This is 
proved by the twelfth, which says: — the water that loiters most dis- 
charges most rapidly the matter that it carries. Therefore the river which 
by meandering more makes itself longer by means of its twists and turns 
makes itself so much slower in proportion as it makes itself longer. 

E 66 V. 

Of the difference that exists between the accidents of water and 
the accidents of air and fire: 

Water is not capable in itself of being either condensed or rarefied, 
34 ' 


but it exists in as great quantity in front of the fish that penetrates it as 
behind it, and it opens itself up as much in front of that which penetrates 
it as it closes up behind this penetrating thing. And the impetus of the 
fish is of briefer duration than that of the bird in the air, although 
the muscles of the bird are very powerful in relation to their quantity; 
because the fish is all muscle and this is very necessary because it is 
in a heavier substance than the air. But although the water is not itself 
capable of being condensed it is of a nature to acquire gravity and levity. 
It acquires gravity at the destruction of the impetus which raises it in 
the air at the creation of the wave, and levity by the creation of the 
impetus that lightens the water and causes it to move contrary to the 
natural course of heavy things. 

OF T H E V A L L E y I N T E R P o S E D B E T W E E N 
THE W A V E S ^ 

The valley interposed between the waves is lower than the general 
surface of the water, as one sees when the water turns back in order to 
fill up the places that have been struck by the water-spouts. ^ ^ 


Of those that take up the whole of this height and of the moving and 
the fixed. Of the long and the round. Of those that change their move- 
ment and those that divide, and those that become merged in those 
[eddies] to which they unite themselves, and those that are mingled 
with the falling and refiex watet and make it spin around. 

Which are the eddies that cause light things to whirl round on the 
surface and do not submerge them? Which are those that submerge 
them and cause them to spin round upon the bottom and then deposit 
them upon this bottom? Which are those that separate the things from 
the bottom and throw them back to the surface of the water? Which are 
the slanting eddies, which are the straight, which are the shallow? 

■ ■ F 2 T. 


When you put together the science of the movements of water re- 
member to put beneath each proposition its applications, so that such 
science may not be without its uses. 

Of the usefulness of the courses that the swimmer ought to follow 


with regard to the surface revolutions of the waters and as to their eddies 
which submerge these swimmers. Then how he ought to direct himself 
when submerged in order to save himself, and so forth. 

And at the end of each book notice the things that are most remark- 
able, as how to break through the thickness of the eddies in any direction. 
Of what measures one ought to take when swimming in a rough sea, and 
how to avoid being dashed against the rocks and on the rudders of ships. 

F 2 V. 

Of the things carried by the water, that will make the greatest 
revolution which is of least size: 

This happens because the great revolutions of eddies are infrequent in 
the currents of rivers and the small eddies are almost numberless, and 
large objects are only turned round by large eddies and not by small ones, 
whereas small objects revolve both in small eddies and large. 

Of objects equal in length and breadth carried by the current of the 
waters, those will make fewest revolutions which are deepest. 

This happens because these revolutions vary greatly from the surface 
to the bottom of the water, in which as many revolutions are produced as 
there is depth to cause them. Wherefore of necessity an object borne by 
the water when it buries itself deeply is buffeted by many revolutions at 
different degrees of altitude; and for this reason it remains in a state of 
hesitance and many times obeys none or if it obeys then it obeys the 
most powerful. 

Of objects equal in shape and size, that which is buried deepest will 

obey least the revolutions of the water. 

. F 3 r. 

Book ten. Of the different recesses and roundnesses that exist in 
reservoirs, before the exits of the water from these reservoirs, with the 
varying rates of speed, sizes, depths and breadths; and the shapes of the 
holes, high or low, wide or narrow; and the walls thick or thin. 

° F4V. 

Book nine. Of the water that passes through a reservoir, of which 
the walls are full of holes of various sizes, shapes and positions, at different 
heights, varying from the entrance to the exit and conversely; and so also 
the reservoir of different shapes, depths, lengths, and breadths; and the 
water more or less powerful and swift, great and small. 

F 5r. 


The flow and ebb is double in the same sheet of water, because it 
will be many times at the mouth of this sheet of water before there is a 
decrease in the great sheet of water; this occurs because the wave of the 
first flow runs strongly in the sheet of water, and during the time when 
this wave follows its impetus that at the mouth makes its ebb. Before the 
wave, penetrating into the neck, feels the ebb at this mouth of the sheet 
of water g the flow starts again at this mouth, and in this time the 
wave, which has penetrated into the neck, pauses, slackening its impetus 
in proportion as the second penetration by the second wave begins 
afresh. Thus so many of these waves enter the neck that the sheet of 
water is raised and its waters come back with impetus behind the ebb 
that recedes from this mouth, and [this ebb] does not penetrate farther 
in the third or fourth wave, so that the first water is not thrust out of 
the entrance. , 

F 6 V. 

In the big wide eddies, the water raises and uncovers the soil heaped 
up in its centre. 

In the small eddies of water, the water bores down and makes a 
hollow in the centre of the eddy. 

Of objects borne by the water upon its bed, the lighter makes a 
longer path in the same time. 

- - — A river does mot 'remain uniform, for after the current it unloads 
shingle, and ^ produces another current, of which the movement 
is directed either to the bankrior the jbo as man;r rjifT^r pni- 

as there are different slopes of the mounds of shingle left at the bottom 
by the aforesaid currents. 

^ F 7 r. 

The depth of the sheet of water which receives the fall of the water 
will always have the shape of a quarter of a hollow sphere, if the soil be 
of uniform resistance. 

And this arises out of what has gone before, where it is stated that the 
straight course of the water is higher and swifter in the middle than on 
the sides; and the greater speed sends its fall more forward than does the 
slower speed. ... ^ ^ ^ 

Given the depth of the fall of the water and its slant, with the power 
of the wheel that is its object, one seeks the height of the fall of this 
water in order to make itself equal to the power of the wheel. 


The water that strikes upon the objects sometimes leaps up con- 
siderably, sometimes only a little, and sometimes it descends, and this 
arises from the objects being small or large, or the descent in front of 
these objects being greater or less, or from the current that strikes these 
objects being more or less powerful. p g ^ 

W A T E R — Q u E S T I 0 N S 

Why the eddies of the water are hollowed in the centre by their 

Why the impressions produced on the surface of the water will main- 
tain themselves for some time, on being carried by the course of the 

Why the movements of the impressions of the waters penetrate each 
other without change of their first shape. 

Rule as to the measurements of water and what breadth, depth, and 
rapidity of movement a given space of current ought to have in a given 
time.' ■ ' - 

Given the resistance of a wheel and given the slant and descent in 
the fall of the water, one asks how great must its volume be to be 
equal to the said resistance. 

Given the volume of the fall of the water and its length and slant, one 
asks whether the power of the wheel is equal to this pawer^fTb-fi 

Given the resistance of the wheel and- the slant of theiwater and its 
volume, onp a«ks thciervgtK rvf tKe fiillr F9r 


Water that pours out through the same-sized mouth may vary in 
extent in a greater or less degree in [various] ways, of which the first is 
that the surface of the water may be either a greater or less distance 
above the mouth through which it pours, the second that the water 
passes with greater or less speed beyond the bank where this mouth is 
made, the third that the side below the thickness of the mouth where the 
water passes may be either more or less slanting, the fourth in the variety 
of slant of the sides of this mouth, fifth in the thickness of the lip of this 
mouth, sixth as to the shape of the mouth, that is whether it be round 
or square, or rectangular or elongated, seventh according as this mouth 
is placed at a greater or less slant of bank in its length, eighth as this 



mouth is placed in a greater or less slant of bank in its height, ninth 
according as it is situated in the concave or convex parts of the bank, 
tenth as it may be placed towards the greater or less width of the canal, 
eleventh if the top of the canal has more speed at the top of the mouth 
or more slowness than elsewhere, twelfth if the bed have round bosses 
and hollows opposite to this mouth or higher or lower, thirteenth accord- 
ing to whether the water that passes through this mouth takes the wind 
or not, fourteenth if the water that falls out of this mouth falls through 
the air shut in on one side or on all except the front, fifteenth as the 
water that falls thus enclosed is deep within its vessel or shallow, sixteenth 
whether the enclosed water which falls makes a long fall or a short one; 
seventeenth whether the sides of the canal where this water descends are 
hollow or protuberant or straight or curving. f 9 v 

Of the eddies of water which frequently turn their revolving move- 
ment backwards: 

Of the falling and the reflex eddies. The eddy sometimes grows in 
power and diminishes in diameter, and sometimes diminishes in strength 
and increases in diameter. 

The first movement is when the water flows away by its base, as the 
water that forms the eddy becomes swifter when it is lower, because 
it has a greater weight of water above it and therefore becomes swifter; 
and because the water pushes downwards more than upwards it restricts 
this void in the eddy more and more; and it bends because it directs itself 
to whether the sheet of water has its outlet. 

F 12 r. 

Water with an uneven bed makes contrary movements from the sur- 
face to the bed. The unevenness in the beds of rivers springs from the 
bends in the banks or from substances that have fallen from these banks 
to their feet. 

F 12 V. 


When the hand is turned in circular movement in a vase half-filled 
with water it causes an accidental eddy which will expose the bottom of 
this vase to the air, and when its motive power is at rest this eddy will 
follow the same movement but it will diminish continually until the end 
of the impetus imparted to it by its motive power. 

F 13 r. 


O F W A T E R 

The eddy with the deeper hollow will be that produced in water of 
swifter movement. 

And that eddy will have a smaller hollow if it is produced in deeper 
water which has not the same movement but is slower. 

And with water of equal speed that will keep a larger hollow where 
a greater depth of water turns with its movement. 

This is said because many times the eddies are produced in a straight 
current in a great expanse of slowly moving water*, and as this water is 
partly supported by the eddy which revolves in a thin coil between it 
and the air of the hollow, this lateral water being of great weight pushes 
upon the sides of the eddy where it is leaning and finding them weak 
compresses them. fijv. 

[Of eddies'] 

If water higher than air acquires weight, as is shown in the seventh of 
the ninth, why is it that the water of the sides of the eddies is higher than 
the bottom of the eddy which up to this point is full of air. 

You have the fourth of the seventh which proves that every heavy 
substance is only of weight along the line of its movement and in no 
other direction; and here you see very deep eddies after the manner of 
great pits in rivers, the sides of which are of water, which is every- 
where higher than the air of this eddy; and these banks of water 
are without weight except by this line of their movement, during the 
time in which they possess the strength given them by their motive 

What produces eddies and why some are hollow at the centre and 
others are not. 

Whether water poured into the hollow of eddies would fill them 
or no, or would escape by the bottom and enter into the current at 
the side. 

Which natural eddies are of considerable depth and which of slight 
depth; which change their position and which do not move; which while 
moving turn in an opposite direction and which keep their movement in 
one direction; which become duplicated and which do not; which unite 
in contrary movements. 

•' P 14 V. 




Write first of the simple hollows made by the simple falls of water 
upon a bed of a uniform substance, and then upon a bed of various sub- 
stances. Then with obstacles placed in the course that the water takes in 
its descent, then with obstacles in the place where it has struck, that is, 
upon its bed; then in its reflex movement, and first at the beginning of 
its fall. Then describe in what part of the edge of the sheet of water this 
water will take its course; and what substances will be carried away or 
deposited in different parts of the bed of this sheet of water; and what 
will be the speed or slowness of movement of the water in various parts 
of the surface, and so also from the surface to the bottom at various 
depths and breadths; and thus you will do as far as the bottom. 

F 15 V. 

\Movements of water] 

Of the parts of the same water that rises through the air at different 
angles, that which has least slant falls back nearer to where it started. 

The rising motions of the water which it makes from the bottom to 
the surface of the sheet of water will never fall back towards the bottom, 
because not entering into the air and not acquiring weight they cannot 
penetrate to the bottom, by the seventh of the ninth. 

The water always rises and descends with a disconnected movement 
of speed, and this is caused by the air that it penetrates and the air that 
is mingled with it. ^ ^ 


It is possible for there to be less depth underneath the current than 
before it or on the sides. 

Let 0 c nh& the current and a an eddy of double strength according 
to the ninth concerning eddies. Since in addition to its revolution it 
strikes against the bank and leaps up into the air, and falling back upon 
the rest of the water penetrates it and strikes and hollows out the bed in 
sudden chasm, for, in addition to the force of the blow, there is joined the 
spiral drilling made by the aforesaid revolution, by means of which what 
has been shaken by the blow is stirred up and carried away; and it 
becomes more powerful as it is more turbid. 

And this is the most powerful method that can be made use of 
in order to dislodge and carry away the soil and so create a great 


Beneath the current the bed will become raised when the course of 
this current dies in stagnant water. 

By the sixth of the ninth — where the course of the water fails, there 
remains that which the water has brought. ^ ^ 

Of a volume of water that has struck upon an object, the lower part 
is the first to strike the bottom and it is instantly reflected to the surface. 
That which is in the middle does not descend to the bottom, but en- 
countering the first part reflected it strikes upon it, and is knocked and 
so it also is bent back in the same lines and revolutions. 

And the two bodies of water when the lower encounters the higher 
unite and revolve together at their contact. 

Of the water that falls into other water that which is nearest the centre 
of the fall slants most and that nearest the extremities is the straightest. 

S U R F A C E w A V E S 

When water strikes other water at a considerable angle the part which 
strikes first is immediately bent back and delays, and that which succeeds 
to it veils it with a thin covering and runs swiftly upon that which first 
slackens and so it is then bent and slackens at the same spot as the fore- 
going. And the water that follows does the same upon it, and so in 
succession each new wave follows its course. 

The turbid running water, if it is high at its start and at its entry into 
the sheet of water, flows for a considerable distance at the height of its 
first impetus before it buries itself or becomes mingled with the other 

F ig V. 

Definition of the half-cylindrical wave and what part of its volume 
has a greater or less slant, and how it commences and ends, and where 
it is more or less wide or more or less high or I would say deep; and the 
differences that there are in it when it is large or small or swift or slow. 

The waters flow one above another without mingling for a long 
space, when their entrance in the sheet of water is higher and swifter in 
the one case than in the other. 

F 20 r. 

Where the water has only slight movement the half-cylindrical waves 
will keep their direction when they intersect. 

Where it is swifter they will curve. 

42. ■ ■■■ 


And where the rates of speed are unequal their curves will vary 
towards the end. f2ov. 

Of the eddies one is slower at the centre than on the sides, another 
is swifter at the centre than on the sides; others there are which turn back 
in the opposite direction to their first movement. 

That eddy is slower at the centre than on the sides which makes a 
great revolution, and this deposits a considerable quantity of matter in 
the centre of its circle and leaves it in the form of a mound. 

The eddy which is swift at the centre of its revolution carries air and 
water in its base, which it hollows out and bores down after the fashion 
of a well, F 21 r. 

Every impression of the water is maintained over a long space and 
this is so much the longer as it is swifter. 

Write of the things worthy of remark that are found in water; and 
what revolutions they make when they are of different shapes and the 
water makes different revolutions. f 21 v. 

Of the different rates of speed of currents from the surface of water 
to the bottom. 

Of the different cross slants between the surface and the bottom. 

Of the different currents on the surface of the waters. 

Of the different currents on the bed of the rivers. 

Of the different depths of the rivers. 

Of the different shapes of the hills covered by the waters. 

Of the different shapes of the hills uncovered by the waters. 

Where the water is swift at the bottom and not above. Where the 
water is slow at the bottom and swift above. 

Where it is slow below and above and swift in the middle. Where it 
is slow in the middle and swift below and above. 

Where the water in the rivers stretches itself out and where it 
contracts. Where it bends and where it straightens itself. 

Where it penetrates evenly in the expanses of rivers and where 
unevenly. Where it is low in the middle and high at the sides. 

Where it is high in the middle and low at the sides. 

Where the current goes straight in the middle of the stream. Where 
the current winds, throwing itself on to different sides. 

Of the different slants in the descents of the water. ^ 23 V. 




Of the waters that cross at different angles in their reflex move- 
ments, and of those that cross on the summits of the waves; those that 
cross the descending wave and those that cross in the trough of the 

Some cross at different angles, great reflex movement with small 
reflex movement, and similarly a great wave with a small one, or falling 
movement with that in the valley or with reflex movement, small with 

Sometimes there is reflex with falling movement, sometimes valley 
with wave, sometimes falling movement with reflex, small and large, 
and at different angles. 

Sometimes rapid waters with slow, sometimes eddies with waves or 
valleys or reflexes, or the falling movements of water flowing along 
different li n es .crQssirLg__Qne_another. 

Courses by different lines ohe^aboveihe other. 

Eddies with different movements whiclf ha-ve-inmieet and enter into 
one another, 

Lengths of different curves of eddies from the surface of the w^f ' 
to its bed as they intersect one another. 

Intersection of falling and reflex eddies. 

Of the waters that are interposed in any direction between the said 
accidents of the waters. 

F 24. r. 

\_Books of the Treatise on JVater'\ 

Book nine of the shapes of the eddies. 

Book ten of the action of the eddies. 

Book eleven of things that aid the eddies. 

Book twelve of things that injure the eddies. 

Book thirteen of the percussions of the waters one with another as 
they leap up within the air at different rates of speed. 

Book of the waters that spring up within the air at different angles 
and with the same speed. 

Book of the waters that spring up within the air and the different 

Water more slanting, striking that less slanting and more powerful 
and less deep. 



Water less deep and more slanting and more powerful than the 
deeper and less slanting. 

Shallow water driven through the air by greater power than the 
deeper water. A 

•T F 24 V. 

Of the waters falling through the air which intersect with various 
depths and lengths of movement and power. 

The reflex movement will never be of the height of the beginning 
of the falling movement unless it strikes as does the wave on the rock of 
the sea. 

[Of the nx)aves\ 

In proportion as the waves of the sea are higher than the ordinary 
height of the surface of its water, so the bottoms of the valleys that lie 
between the waves are lower; and this is due to the fact that the great 
fall of the great waves creates the great hollows of the valleys. ^ v 


Here follows the proof of what is said on the opposite page: 

I say that no part of the surface of water moves of itself unless it 
descends, therefore as the sphere of water has not the power to descend 
in any part of its surface, it follows from the first conception that it does 
not move of itself. And if you carefully consider each minute particle 
of this surface you will find it surrounded by other similar particles 
which are at an equal distance between them from the centre of the earth, 
and at the same distance from this centre is that particle which is sur- 
rounded by them; therefore, by the third conception, that particle of the 
water will not move of itself because it is surrounded by edges of equal 
height. And thus every circle formed of such particles makes itself a 
vessel for the particles enclosed within this circle, which vessel has the 
circle formed by its edges of equal height; and in this respect this particle 
resembles all the other similar ones of which the surface of the sphere of 
the water is composed. Of necessity it will be without movement of itself, 
and in consequence each being at equal height from the centre of the 
world, necessity makes their surface spherical, but it is not necessary that 
they should be spherical below, as reason and experience show. 

That which is said of the surface of the water that borders on the air 
is understood to be said of the surface of the air that borders on the 


fire, which would be such as often to evaporate after the manner of 
clouds drawn by the heat of the sun, as does the water drawn through 
the air by the same heat in the form of clouds; and in the same way the 
fire drawn by a greater heat than its own, that is to say by the sun, it 
being proved in the sixth that it is warm by essence and not by virtue, 
as many would have it. 

So having proved by the testimony of these spheres that the flexible 
elements are spherical, it is my purpose to investigate nature both in its 
universal aspect and in the particulars of each of its elements, and first 
of fire, then of air, and then of water. f 26 v 

Book thirty-two. Of the movement that fire makes when it pene- 
trates the water at the bottom of the boiler: 

It runs bubbling to the surface of this water by different ways and 
according to the movements that the water makes when struck by the 
penetration of the fire. By means of this experiment you can investigate 
the hot vapours which are exhaled from the earth and pass through the 
water, twisting themselves about because the water checks their move- 
ment, vapours which afterwards penetrate through the air in straighter 

And this experiment you will make with a square glass vessel, keeping 
your eye at about the centre of one of these walls; and in the boiling 
water with slow movement you may drop a few grains of panic-grass 
because by means of the movement of these grains you can quickly know 
the movement of the water that carries them with it. And from this 
experiment you will be able to proceed to investigate many beautiful 
movements which result from one element penetrating into 

F 34 V. 


The water that falls from the cloud is sometimes dissolved into such 
minute particles that by reason of the friction that it has with the air it 
cannot divide the air but seems to change itself into air. Sometimes in 
descending it multiplies, because it finds the minutest particles of water 
which by reason of their lightness were of slow descent, and becomes 
incorporated with them, and at every stage of its descent acquires a new 
quantity of water. Sometimes the winds bend the rain and so cause its 
descent to be slanting, and for this reason the descent becomes slow and 



protracted, and it frequently happens that it is converted into such fine 
particles that it can no longer descend and so remains in the air. 

\Treatise on water\ 

Write how the clouds are formed and how they dissolve, and what it 
is that causes vapour to rise from the water of the earth into the air, and 
the cause of mists and of the air becoming thickened, and why it appears 
more blue or less blue at one time than at another. Write in the same 
way of the regions of the air and the cause of snow and hail, and how 
water contracts and becomes hard in the form of ice, and of the new 
shapes that the snow forms in the air, and of the trees in cold countries 
with the new shapes of the leaves, and of the pinnacles of ice and hoar- 
frost that form new shapes of plants with strange leaves, the hoar-frost 
serving almost as the dew ready to nourish and sustain the said leaves. 

F 35 r- 

No surface of water that borders upon the air will ever be lower than 
that of the sea. 

The wave that the motive power makes before it in the air or between 
the surface and the bed of the water is in the shape of a half sphere. 

The wave made by the motive power on the surface of the water is 
in the shape of a half-circle, and towards the bottom it has the shape of a 

Why the movement made by the motive power on the surface of the 
water makes a wave before it, and does not do so when it moves between 
the surface of the water and its bed. What one asks occurs because the 
water of the surface borders on the air, whereas the water that is between 
the surface of the water and its bed borders on the water that is above 
and the water that is below. f 41 r 

Of the water that falls from the weirs of rivers, that part will have its 
straight course shut in which has the most powerful fall: 

This comes about because water with a powerful fall hollows out the 
soil of the spot on which it strikes and deposits it where its course is more 
feeble than beneath the reflex movement of the water; this as it moves 
towards the sky becomes more feeble with each degree of its movement 
until at last it loses all its power. 

And as in this reflex action its power ebbs it lets fall below it all the 
things of weight taken from the spot where it h^s struck, and after this 

/ ' ■■ ■ 47 :'. 


inundation the water becomes lowered and finds itself shut in between 
the matter which it formerly carried and the bank from which it has 

Of the waters that descend in torrents from the weirs of rivers only 
that will preserve its straight course beyond this torrent of which the 
fall was feeblest and slowest. 

This happens because that which moves slowly strikes feebly, and 
therefore it follows that it only raises itself a little from the bed on which 
it strikes, and in consequence deposits but little in the reflex movement 
of the water. And this is why after this deluge the bank here remains 
low, and all the water that falls follows its course where the bank is 
lower, and consequently the straight course of all the water of the river 
will remain with the water that has a feeble fall. ^ 

Of the things borne by the water which have part of themselves in . 
the air and part in the water: 

If a thing is borne by the water being half in the water and half in 
the air, and the air moves with a speed equal to the speed of the water, 
then this movable thing will be in the first stage of swiftness of movement. 

If the air is slower than the movement of the water which moves in 
the same direction as the air, the movement of the movable thing will be 
slower than if these movements of air and water were equal, and it will 
be so much slower in proportion as these movements of air and water 
are more different. 

If the movement of the air is swifter than that of the water^ which 
moves in the same direction, then this movement of the object will 
become more rapid, and the more so as this air is swifter than the water. ^ 

If the movement of the air against the course of the water is of equal 
speed to that of this water against the air, the movable thing will follow 
the course of the water if it has more contact with the water than with 
the air: it will do the contrary if it has more contact with the air than with 
the water. 

F43 V, 

How a leaf is whirled about along different lines in the depth of the 

This movable thing revolves along different lines, high and low, 
turning itself over or not turning over, and doing the same in the width 
^ M.S. aria. 


of the water which moves it. And this springs from the different move- 
ments of the water with its different slanting and eddying courses. Here 
one may place objects of different shapes, and one will have made a good 
experiment tn'^ ... by the leaves of the trees which are borne in con- 
siderable quantities from the surface to the depth of the flowing and 
transparent waters. F44r 


To set forth the conditions of the waters that spring forth within the 
air, and their percussions made with different degrees of power, quan- 
tity, length of movements and variety of slant, I will institute a compari- 
son between the four principal winds, namely: north, south, east and 
west; and with these conditions I shall equip myself to give information 
as to the aforesaid movements of the water within the air; as a result this 
description will be briefer and more expeditious. f 45 r 

These are the four ways in which the waters moving in the same 
manner penetrate one another with lines that slant towards the centre 
of the earth. 

These four demonstrations are sufficient to prove the four principal 
effects that the waters produce as they strike one another within the air. 
Of which the first is that in which the more slanting penetrates the less 
slanting, and penetrates it in part and carries with it the part that has 
been struck. 

In the second demonstration the less slanting penetrates the more 
slanting in part and carries with it the part that has been struck. In the 
third demonstration the more slanting water carries away with it entirely 
the less slanting water. The fourth does the opposite, in that the less 
slanting water carries away with it entirely the more slanting. 

If the earth were [not] spherical no part of it would be uncovered by 
the sphere of the water. 

You will never find a flat piece of the earth without the water upon 
it being of convex shape standing in the middle of this level surface. 
And this water will never move towards the extremities of this plain. 
Therefore upon a surface that is absolutely flat there may be water of 
varying degrees of depth. 

^ Words erased in MS. 


It is impossible to find any flat part in the surface of any very great 
expanse of water. 

The deep recesses in the ocean bed are everlasting, the summits of 
the mountains are the contrary: it follows that the earth is spherical and 
all covered with water and that it will be inhabitable. 

An object which is carried by the course of the water ... in the 
course of less power: if it is slanting below it will move towards the 
bottom, and so it will move according to the direction of its slant. 

Of the objects carried between two currents of water only that one 
will proceed without being turned upside down which is in the middle 
of two currents of equal movement. 

But that will be in continual revolution over and over which is in the 
middle of two unequal currents. 

An object will not make any lateral revolution when it moves 
between currents equal in movement; and so conversely. f 52 v 

Of the movement of a thing that slants irregularly in water which 
has a regular current: it will proceed to turn continually when below 
the surface of the water, and that in which the slant is regular will not 
make any turn. 

When the upper part of the straight side of the object and the lower 
part are struck by an equal current this object will make a lateral 

F 53 V. 

\T he percussion of water\ 

All water after it has struck against an object is divided into four 
different and principal movements, namely right and left, high and low; 
and the low movement causes injury to its bed. 

Of the four principal movements which water makes as it divides 
in its reflex action, that will be more rapid which is reflected at a more 
acute angle. 

^ F54r. 


Of the things carried by the course of the waters that which has a 
larger part of itself in the air responds to the movement of the air more 
than to that of the water ; and so conversely that which has a larger part 
of itself in the water will follow the course of this water more than that 
of the air. 



See in the windings of the canals where the water is swifter below, 
in the middle, and above, and of this make a book. 

The pipe by which water is drawn to a height receives less damage 
than that pipe along which water is driven; and this is due to the fact 
that in the first case the motive power is above and in the second it is 

Where the water is most rapid, it wears away most the bed on which 
it rubs. 

Where the water is most shut in, it becomes most rapid and in its 
passage wears away its bed most. F65 r 

The object always changes the order of the nature of the waves that 
have been commenced. 

The current a b has one order and the object which receives its 
percussion throws it over completely and changes it to another figure. 

If you wish to form a correct impression of all the shapes of the 
waves and the courses of the waters, observe the clear water where it is 
shallow beneath the rays of the sun, and you will see, by means of this 
sun, all the shadows and lights of the said waves and of the things carried 
by the water. 

The sphere of the water increases and decreases sensibly or insensibly, 
according to the greater or less, more universal or less universal deluges 
of the waters given back to this sphere of the water. f 65 v 

E D D I E s 

Eddies are always the intermingling of two streams of water, that is, 
the falling and the reflex. 

All the water which in the currents of the rivers tarries behind the 
objects in these currents has no other exit than by contact with the 
aforesaid currents. 

The eddies which turn back are always those of the swiftest water. 

And the eddies that are turned in the direction that the stream is 
flowing are those of the water which tarries in the stream’s course. 

Here the law of the waters in their eddies does not fail, because the 
water that becomes slow, turns back, and makes the eddies in the 
opposite direction to its movement, as do the eddies of the swiftest water. 
And for this reason these eddies, whether of the slow or of the rapid 
water, mingle together and redouble their power; but not entirely 

..51, ■ 


because the slow eddy in mingling with the swift becomes swifter than 
at first, and the swift eddy as it embraces and unites with that which 
is slower acquires slowness. 

The hollow in the swift waters caused by the submersion of the 
eddies will point towards the approach of the waters, and in the slow 
waters it will point in the direction in which they are flowing. 

F 66 r. 


A drop is that which does not detach itself from the rest of the water 
unless the power of its weight is more than its adhesion to the water with 
which it is joined. 

That drop is formed more slowly which has a slower movement of 
water at its creation. 

All the movements made on the surface of water are also made at 
each successive stage of its depth, and likewise in each part of its length; 
and this is learnt from the grasses that grow on the beds of the streams. 

F 66 V. 

Water that falls in the air separates itself with difficulty from its bulk, 
and the sign of this is found in the curve that it produces and the winding 
of one of its parts round the other, between which the film of water is 
interposed. ^671. 

If the earth covered by the sphere of the water is more or less heavy 
than if it were not so covered: 

I reply that the heavy substance weighs more which is in the middle 
of the lighter. 

Therefore the earth which is covered by air is heavier than that 
which is covered by water. 


I say: ■— the centre of gravity of the pyramid being placed at the 
centre of the earth, it will change its centre of gravity if it is subsequently 
covered in part by the sphere of the water, and I give an example with 
two cylindrical weights that are equal and similar, of which one is half 
in the water and the other entirely in the water: I say that that which is 
half out of the water is the heavier, as has been proved. 

Suppose there to be a straight line equal to the diameter of the 
sphere of the water, which touches the surface of the sphere of water in 
the centre of its length. One asks what is the difference between each 


of the miles of the descent which the surface of this sphere makes below 

the said line. ^ ^ 

F 69 r. 

[Centre of the earth and watery sphere] 

Because the centre of the natural gravity of the earth ought to be in 
the centre of the world the earth is always growing lighter in some part, 
and the part that becomes lighter pushes upwards, and submerges as 
much of the opposite part as is necessary for it to join the centre of its 
aforesaid gravity to the centre of the world; and the sphere of the water 
keeps its surface steadily equidistant from the centre of the world. 

Where the sun is straight above, the earth grows light; covered by 
the air, the waters and the snows have been lacking to it, and on the 
opposite side the rains and the snows have made the earth heavy again 
and drive it towards the centre of the world, and thrust the parts that 
have become lightened to a greater distance from, this centre; so there- 
fore the sphere of this water preserves an equality of distance from the 
centre of its sphere but not of gravity. 

Water poured in the air at a concave angle becomes spread out in a 
sheet, and it remains spread out in a sheet more on the side of the angle 
where this water makes more contact; and on the opposite side the sheet of 
water will leap up and make its union at first in the form of an open sheath. 

F 70 r. 

[Water of the sea and of rivers] 

The sea beneath the equinox is raised by the heat of the sun, and 
acquires movement over every part of the hill or portion of the water 
that rises in order to give equality and restore perfection to its sphere. 

If an outlet of water with sixteen ounces descent in each mile yields 
me sixteen measures of water, how much will the same outlet afford with 
eight ounces descent per mile? 

The revolutions of the cross-eddies acquire size and slowness at each 
stage of their length. 

The convulsions of the reflex movements of the water at the bottom 
of rivers destroy the circling movements of the longitudinal eddies. 

The water of the sea and of the turbid rivers is heavier than the 
other waters, and as a consequence offers more resistance to the weights 
it carries. 

The water of the sea offers more resistance because the weight of the 
salt that is mixed with it is liquefied, and it is inseparable from it without 


the heat that dries up the water; but the turbid part of the water is 
separated from it by heat and when the water is at rest. f 70 v 

[Movement of water in the air and in the water^ 

The movement that water makes in the air follows for some distance 
the line of the sides of the small holes through which it descends. It is 
not thus with the discontinuous quantity that the stone shows itself to 
be when thrown by the circular movement of the man’s arm; this follows 
the straight movement; which the water does not do on account of it 
being spread out in a sheet, for this in a long space of movement collects 
all the parts of the water together. 

The impressions of the movements made by the water within the 
water are more permanent than the impressions that the water makes 
within the air; and this takes place because water within water is devoid 
of weight, as is proved in the fifth, but only the impetus weighs and this 
moves this water that has no weight until it is itself consumed. 

The impressions of the movements of water are more permanent 
when the water carried by the impetus enters into a sheet of water 
[felago) with slower movement, and conversely. 

The impressions made by the water within the air are destroyed in 
the first movement that they make towards the earth, because the im- 
petus is consumed in the natural movement that is produced in the water. 

■ F 71 r, , 

O F T H E M O V E M E N T S O F W A T E R 

The falls of water that intersect in the air become filled with air in 
their reflex movement. 

Of the falls of water which strike each other within the air being of 
equal thickness, that which descends from a higher part of its reservoir 
will join itself to the course of that which is lower and will complete its 
course with it. 

Falling water which then runs over terraces breaks its bed very 
much at the end of these terraces. 

This proceeds from the fact that when the current of the water 
reaches the last stage of these terraces it falls and raises itself from the 
bottom, burying itself so much the more as its fall is deeper, because the 
fall is more powerful in great descents than in lesser ones. 

All water, when it strikes the bottom or upon another object, divides 
and runs in different directions. 


All water, when it surges up, divides at the surface and runs in different 
directions, and so much the more as the sheet of water is more tranquil. 

F 71 V. 

The simple movements of the waters are those which act simply with 
their simple movement of whatever kind it may be. 

Composite movements are created by different movements and 
these are very powerful in different functions. 

The wave is slower at the summit than upon its sides. 

The falling movement is more rapid than the reflex. 

Joined together, the greatest and the least slowness of the waves, that 
is of the wave in itself with its sides and summits, become equal to the 
common course of their stream, and this is to be adduced in the con- 
clusions, that is to say to prove them. f 72 r 

\Of the raising of wafer in nature and by artifice^ 

If the water which gushes forth from the high summits of the 
mountains comes from the sea, the weight of which drives it up there so 
that it is higher than these mountains, why has this portion of water the 
capacity of raising itself to so great a height, and of penetrating the earth 
with such difficulty and length of time, while it has not been granted to 
the rest of the element of water to do the same, although this borders on 
the air which would not be able to resist it and so prevent the whole from 
rising to the same height as the aforesaid part.? 

You who have found such an invention must needs return to the 
study of natural things, for you will be found lacking in cognate 
knowledge, and of this you have made great provision by means of the 
property of the friar of which you have come into possession [?].^ 

Water falling into a channel of width equal to the width of the water 
that falls will make a deep hollow within the surface of the water. 

Water falling into [a channel] where the width is greater than the 
said fall will not make a very great hollow in the surface of the water, on 
account of the eddies, which cause the water to bend in the hollow 
caused by this fall. 

Water which clears away the bottom on which it hurls itself rapidly 

^ Ravaisson-Molliensays: ‘Cette phrase signi fie peut-etre: Si tu as trouve k inventer une 
imitation de I’elevation de I’eau dans la Nature, aux cimes des monts, en ayant cru beaucoup 
t’instruire a cet egard avec le fonds de livres, dessins, etc., du frere [moine] un tel, que tu 
possedes, cette instruction-lk te trouvera bientot en ddfaut, et il te faudra de nouveau 
etudieiTes choses de la Nature.’ 



or slowly in all its width, depth or narrowness, its seething mass being 
tossed back by the bed of the watery expanse, is in part caught up again 
to the surface of the water, there to make its various falling and reflex 
movements, in part returns to where was its first fall, burying itself there 
with it and then returning up in lateral eddies, and in part falling back in 
the middle of the seething mass and spreading itself out with slow 
movement round the centre of its fall. p v and r 

\Movements of ns)ater\ 

Between the current and the eddy is the sand. 

Between the sand and the eddy is a smooth valley where the eddy turns. 

In the eddy are pieces of timber and other light things. 

If the air is motionless an object borne on the surface of the water 
will be slower than one that is below its surface. 

Where the water issues forth by a level bed beneath the sluices it 
hollows out the bed before and behind these sluices. 


A wide object borne by the current of the river between the surface 
and the bed of the river, if it should meet with water that is slower than 
that which bears it and should find itself at that time slanting in the 
direction of the approaching river, will immediately leap from the bed 
to the surface of the water; and if this slant is pointing in the opposite 
direction to the course of the water then in encountering the slow 
current it will suddenly precipitate itself towards the bottom; and if this 
slant looks to the right or left of the breadth of the stream it will throw 
itself to this right or left side of the stream and so will continue in any 

F 78 r. 


If the mountains had not remained in great part uncovered by the 
waters, the courses of the rivers would not have been able to carry so 
much mud into the sea as exists at a great elevation, mingled with the 
animals which have been enclosed by it. 

The revolutions of the reflex water in returning to the current of its 
river penetrate it more in its lower parts than on its surface; and this 
proceeds from the fact that the current, by the seventh, is swifter above 
than below, and is in consequence more powerful above, and therefore 
less penetrated by the percussion of this reflex water above than below. 



The eddies formed by the percussion of the reflex water in the course 
of the falling water are of two kinds, of which one is produced towards 
the bottom and revolves vertically through the length of the stream, 
the other is upon the surface and revolves right and left through 
breadth of the stream. The lower is produced by the falling down 
again of the seething mass towards the bottom, and that on the surface 
by the revolving movement striking into the surface current. ^ ^ 

Water turns before falling water like the wheel of a mill. 

° F 8i r. 

Of the surfaces surrounding the water that is poured through the air 
from an expanse of water, and also what the water does in these surfaces. 

Of the movements of the things that have fallen with the water which 
moves in the air, and also what they do in this expanse of water. 

Of the things that float upon the middle water, and how they 
become submerged when they find themselves between the centre of 
the middle water and the fall, and they become submerged together 
with this fall which takes place in the expanse of water, and strike against 
the bottom and break in pieces. 

Write therefore all the effects of the things that become submerged 
in any extremity of this middle water, which always submerges its 
extremities because it is in the centre of all the reflex movements towards 
the bottom of its expanse of water. 

^ F 8l V. 

Of the earth. Every heavy substance tends to descend, and the lofty 
things will not retain their height but with time they will all descend, 
and thus in time the earth will become a sphere, and as a consequence 
will be completely covered with water, and the underground channels 
will remain without movement. 

Of the convex wave. If the wave created by the fall of the water 
of a canal of uniform breadth and depth will be of long movement or 

Of the concave wave. If the concave wave created by the water 
that falls abruptly from the open canal under a sluice will be of long 
movement in a canal of uniform breadth and depth. f 84r 

Water which runs through a canal of uniform emptiness and fills 
all its first smooth part, will fill all the other straight and slanting parts 
and will move with equal swiftness. 

, , ' ' ■ ■ 57 


The movements of the heavy elements are not to the centre in order 
to go to this centre, but because the medium in which they are cannot 
resist them, and when they find resistance in their element this body 
no longer has weight and does not seek to penetrate to the centre. 

Water in air weighs and descends by the shortest path. It divides 
and opens the air which is below its centre of gravity with all its parts 
equally, and it does not divide the air that is upon its sides because it is 
not situated above it. And because of this it makes a hollow in the air 
of very short length until it reaches that which resists it; and as this 
resistance is that of water the water that falls through the air no longer 
seeks to go the centre, because it no longer divides the water as it did 
with the air; therefore the heavy substance moves downwards where it 
meets with no resistance, and not in order to go to the centre. 

F 86 V. 

Write first of all water in each of its movements, then describe all 
its beds and the substances in them, adducing always the propositions 
as to the aforesaid waters, and let the order be good as otherwise the 
work will be in confusion. 

Describe all the shapes that water assumes, from its largest to its 
smallest wave, and their causes. o 

’ F 87 V. 



If with a sluice the larger body of water is divided by the narrower 
and the movement of the water is from the narrower to the larger, the 
water which rises under the sluice will leap on to the larger water, and 
by its falling back it will hollow the bed of the canal in several places 
with different leaps. 

^ F 88 r. 

[Treatise on water] 

Describe what water does in each defined instance between its sur- 
face and the bottom. And what part of the water is slower or more rapid. 

Of the lateral objects placed upon the banks of winding rivers. 

Of the intersections that the waves make one with another on being 
bent back by the opposite banks of the rivers. 

Of the elevation of the waves formed by the intersection of other 
cylindrical waves. f 8 r 



Of the various breadths of the transversal interpositions set in the 
middle of the breadths of rivers. 

Of the various projections of the lateral objects set upon the banks 
of rivers. 

Of the different slants placed in the middle of the widths of rivers. 

Of the different juxtapositions of the fronts of the lateral objects 
placed upon the banks of rivers. f 89 v 

[Book of the treatise on ‘water\ 

If the cylindrical wave shall strike the eddies produced about one 
of the extended banks, these pent-up eddies will be contracted and 
acquire great power to excavate beneath the bank and cause it to fall in. 

Order of the book. 

Put at the beginning what a river can do of equal depth and slant 
of bed on its bank, where lie objects of various kinds. Then place these 
objects two by two. Then place them to face the opposite bank, in the 
same variety, and describe what the waters do when they intersect one 
another in the centre of the stream, and the obstacle they afford to the 
water reflected by the opposite bank. And then describe what each does 
in its bed, that is how it rises and settles itself. 

The side of the wave when it makes its rapid falling movement is 
the end of the slow reflex movement. It follows that the movement of 
the valley of the wave is swift and the crest of the wave is slow. ^ ^ 


If the course of the river is contracted on one of its sides it produces 
a half-cylindrical wave which is swift; and the eddies which are pro- 
duced between the contracted bank and the cylindrical wave occasion 
the laying bare and crumbling away of this contracted bank. 

If the banks should contract equally on each side of the current and 
opposite, then the cylindrical waves will intersect, and after this inter- 
section they will descend and strike upon the bank and cause it to fall 

But if the contraction of one bank should be lower than that of the 
other, then the upper cylindrical wave can enter under the lower. 

Here it is necessary, in the commentary, to define the distances of 
the contractions of the banks and their breadths. 


\^0f canals^ rivers and eddies\ 

The bank which is made to curve inwards in order to give greater 
breadth to the canal is the cause of the sudden forming of an eddy, and 
this bores down and makes a deep hole at the base of the bank and so 
becomes the cause of its fall. 

This is proved by the first of the third, which shows that the river 
in acquiring sudden breadth of space acquires also sudden breadth of 
water, and the water thus widened comes also to lower itself in depth; 
and so it suddenly creates a current which hurls itself upon the bank 
where it has been widened, and striking it divides itself into two eddies, 
one of which (the more powerful, as r ^ in order to be enclosed 
throws itself vigorously straight towards the bottom; and by the ninth 
which says that as the eddy will be most easily penetrated which has the 
lips of its mouth least slanting, it will have them quite straight. 

Water brings about the fall of that bank of which the canal acquires 
a sudden breadth. 

If the canal gains on each side sudden breadth it produces eddies on 
each side; if these are united at the centre of the breadth of this canal it 
will make of itself a sudden and great depth. 

All these figures have to result from experience. f 91 v 

[Cylindrical wave s'\ 

The more the half-cylindrical wave moves the more it descends, and 
the more it spreads itself out the swifter it becomes. 

When there are two unequal cylindrical waves of which the larger 
comes into existence before the smaller, this smaller wave intersects the 
larger and passes above it. And this happens because the larger which is 
created first, when it is opposite to the smaller, is spread out and lowered, 
and the lesser which strikes it, being high, strikes the lowness of the 
greater one, and not finding any obstacle as high as itself runs over it and 
falls headlong on the opposite side and follows its initial impetus. 

But if the lesser of the unequal cylindrical waves starts higher in the 
river than the greater, then this greater follows its natural course, and 
the lesser follows the course of the greater. 

^ F 92 r. 

If the cylindrical waves clash and do not intersect as far as the centre, 
the middle part which clashes leaps back and passes above the part that 
does not clash. 



When two cylindrical waves of equal size and power clash absolutely 
they each turn back completely without any penetration one of the other. 

But if the cylindrical waves are unequal in size, neither the larger nor 
the smaller will observe their law, because the larger does not bend and 
the lesser unites with the larger. 

But if when the waves are equal the rise of the one is before that 
of the other, their blows will not be delivered with equal power; 
consequently the course of the second will bend before that of 
the first. 

F 92 V. 

Water that moves between a bank and a straight smooth bed will not 
make a wave of any kind. 

What is thus stated takes place because a wave is only created by a 
reflex movement,- and the reflex movement arises from the percussion 
of the falling movement which is made upon the particular object at 
the bottom or the sides of the canal; and if in these places there are no 
particular objects then by what has been said it will not create any wave, 
this water being made by minute upward movements which only raise 
themselves a little from the bottom, so that they do not make waves by 
coming to the surface. 

The simple half-cylindrical wave is formed upon some small object 
that is joined to the bank; the water that strikes it there makes a long 
wave in the shape of a half-column which takes its course slantwise 
towards the opposite bank, and dies there and is reborn. 

Let a be the object, placed upon the bank a 0 oi the canal n 0 m p, 

I say that the water which strikes upon this object will make a wave 
which by its being continually reformed will also make itself continuous; 
and it would be always so if it were not interrupted by the common 
course of the water of the canal, which all strikes on this wave and drives 
it unceasingly in every stage of its length, so that at the end it directs it 
according to its ordinary course. f 93 v. 

[Currents and falls of water'] 

In water of ordinary speed the middle water will have tiny ripples. 

The water that is interposed between the mean of the surface and its 
bed is not of the nature of the mean; whereas this mean of the surface 
receives the percussion of the falling and the reflex; for the one and the 
other to be within the boundary falls upon the other water, making 


percussion of the air as of a heavy thing, and as a heavy thing it 
penetrates within the other water struck by it. 

The water falls at first, rises up again, and raises itself with its semi- 
cylindrical wave above the semi-cylindrical wave opposite which made 
its fall more slanting. ^ ^ 

\The current of river s\ 

Water that descends in a straight river moves always by a slanting 
course, from the centre to the opposite banks and from these opposite 
banks to the centre of the river. This is proved by the ninth of this 
where it is stated: The course of straight rivers is always higher in the 
centre of their width and upon the sides than it is between the centre of 
their width and these sides. And this was proved by the seventh in which 
it was stated: — The water of straight rivers never flows in a straight line 
because it is so much swifter as its obstruction is farther removed from 
the banks. And this was confirmed where I said: — Where the falling 
movement is impeded there the reflex movement is created; and by the 
tenth of this: Always between the falling and the reflex movement is the 
maximum depression in the expanse of the rivers; and by the eleventh: — 
After the last height of the reflex water there is produced the beginning 
of the falling movement; and by the twelfth :— The falling movement of 
the waters does not change into the reflex movement without percussion 
against the bed or the bank of the river. Where the water strikes the 
bed or the bank of the river there the soil of the bed or the bank of the 
river becomes raised. 

Always under the falling movement the bed of the river becomes 
raised and its height is restored under the reflex movement. 

The lateral slants of the waters which move continually in straight 
rivers are of a greater or less degree [of slant] according as these waters 
have a more or less rapid current. 

^ G 14 V. 

[Density of water — fresh and salt] 


The Ocean does not penetrate within the earth, and this we learn 
from the many and varied springs of fresh water which in various places 
of this Ocean penetrate from the bottom to its surface. The same thing 
also IS shown us by the wells, made at a distance of more than a mile 


from the said Ocean, which are filled with fresh water; and this takes 
place because the fresh water is lighter than the salt water and as a 
consequence more penetrating. 

Which weighs more, water that is frozen or water that is not frozen? 

Fresh water penetrates more into salt water than salt water does into 
fresh water. 

That fresh water penetrates farther into salt water than salt water 
does into fresh is shown us by a thin cloth, dry and old, that hangs with 
its opposite ends at an equal depth in two different bodies of water, of 
which the surfaces are equally low; you will then see how the fresh water 
will raise itself so much higher up on this piece of cloth than the salt 
water, as it is lighter than it. 

’ ^ G 38 r. 

F O R T H S U D D E N L Y U P O N I T S D R Y B E D 

The course that the water takes when issuing from a lake into a dry 
river-bed is so much slower or swifter as the river is wider or more 
confined or in a more level position in one place than in another. 

By what is set forth the flow and ebb of the sea which enters from the 
Ocean into the Mediterranean, and of the rivers that contend with it, 
raises their waters so much the more or less as the sea is more or less 

G 48 r. 


Pliny says in his second book, in the hundred and third chapter, that 
the water of the sea is salt because the heat of the sun scorches and dries 
up the moisture and sucks it up, and thereby greatly increases the salt 
savour of the sea. 

But this cannot be admitted, because if the saltness of the sea were 
caused by the heat of the sun there is no doubt that the lakes and pools 
and marshes would be more salt in proportion as their waters have less 
movement and depth, but, on the contrary, experience shows us that the 
waters of these marshes are entirely free from saltness. It is also stated 
by Pliny in the same chapter that this saltness might arise because, after 
the subtraction of every sweet and tenuous portion such as the heat 
readily draws to itself, the more bitter and coarser portion will be left 
behind, and in consequence the water on the surface is sweeter than that 
at the bottom. But this is contradicted by the reasons given above, 



whence it follows that the same thing would happen with marshes and 
other tracts of water which become dried up by the heat. It has also 
been said that the saltness of the sea is the sweat of the earth, but to this 
we may reply that then all the springs of water which penetrate through 
the earth would be salt. 

The conclusion therefore is that the saltness of the sea is due to the 
numerous springs of water, which in penetrating the earth find the salt 
mines, and dissolving parts of these carry them away with them to the 
Ocean, and to the other seas from whence they are never lifted by the 
clouds which produce the rivers. So the sea would be more salt in our 
times than it has ever been at any time previously; and if it were argued 
by the adversary that in an infinite course of time the sea would either 
become dried up or congealed into salt, to this I reply that the salt is 
restored to the earth by the setting free of the earth which is raised up 
together with the salt it has acquired, and the rivers restore it to the 
earth over which they flow. 

But to express this better — if it be granted that the world is ever- 
lasting it must needs be that its population also will be everlasting; and 
that therefore the human race has perpetually been and will be con- 
sumers of salt; and if the whole mass of the earth were composed of salt 
it would not sufiice for human food. And for this reason we are forced 
to conclude either that the substance of the salt is everlasting as is the 
world, or that it dies and is renewed together with the men who consume 
it. But since experience teaches us that it does not die, as is shown from 
the fact of fire not consuming it, and from water becoming more salt in 
proportion as it is dissolved in it, and from the fact that when water 
evaporates the original quantity of salt remains, there must needs pass 
through human bodies as urine or perspiration or the other excretions 
that are found there as much salt as is brought every year into the cities. 
And therefore we may say that the rains which penetrate through the 
earth are what carry back underneath the foundations of cities and their 
peoples through the passages of the earth the saltness taken from the 
sea; and that the change in the position of the sea which was over all 
the mountains has left the salt in the mines that are to be found in these 

As a third and last reason we may say that salt is in all created things; 
and we may learn this from passing water through ashes and the refuse 
of things which have been burnt, and from the urine of animals and the 



excretions which proceed from their bodies, and the earth into which by 
corruption all things are changed. 

” ® G 48 V. and 49 r. 


The subterranean courses of the waters like those which are made 
between the air and the earth are those which unceasingly wear away and 
deepen the beds of their courses. 

The soil carried away by the rivers is deposited in the ultimate parts 
of their courses; or rather the soil carried away by the high courses of the 
rivers is deposited in the ultimate descents of their movements. 

Where fresh water is rising to the surface of the sea it is a manifest 
portent of the creation of an island which will be uncovered more slowly 
or more rapidly as the quantity of the water that rises is less or greater 
in amount. And this island is produced by the quantity of earth or 
deposit of stones made by the subterranean course of the water in the 
places through which it flows. 

° G 49 V. 


The falls that the waters make at their banks always wear away the 
bases of these banks and cause them to fall headlong on their foundations. 
This is proved > if the height of the bank a c from which falls the water 
a fly striking and consuming the place struck mn Cyht the centre of the 
percussion upon which are divided the reflex movements n m 0 and 
n c by which in each direction consume the bank that is chafed by their 
revolving movements, then as the banks find themselves thus consumed 
their supports collapse on the side on which their prop fails. 

The water which falls from abto nm will proceed to deepen all the 
bed from where it falls as far as the lowest level of the place where it 
falls, from to c i/. 

’ G 50 V. 



The water of the sea cannot penetrate from the roots to the summits 
of the mountains which border upon it but only raises itself as far as the 
aridity of the mountain' draws it. And if on the contrary the rain which 

della vibratio della terra. 

® MS. monte. So Richter. Ravaisson-Mollien reads mondo. > 

.'E 2 ■ " ... . 65 


penetrates from the summit of the mountain to its roots which border 
on the sea, descends and softens the opposite slope of the same mountain, 
and draws the water continually as does the syphon which pours through 
its longest side, it must be this which draws up to a height the water of 
the sea; thus if s n were the surface of the sea and the rain descends from 
the summit of the mountain a to non one side of it and descends on the 
other side from a to this without doubt would be the method of 
distillation of a filter or as happens through the tube called a syphon; 
and the water which has softened the mountain by the great rain which 
descends from the two opposite sides would constantly attract the rain 
anon its longest side together with the water of the sea, if the side of the 
mountain a m were longer than the side a n\ but this cannot be because 
no part of the earth that is not submerged by the ocean can be lower 
than this ocean. cyor 

\W it h drawings] 

These convolutions must be made with coloured water falling blindly 
into clear water. 

G 90 V, 

Running water has within itself an infinite number of movements 
which are greater or less than its principal course. 

This is proved by the things supported within two streams of water 
which are equal to the water in weight. If the waters are clear they show 
well the true movement of the waters that conducts them, because 
sometimes the fall of the wave towards the bottom bears them with it 
so that they strike upon this bottom; and they would be reflected back 
with it to the surface of the water if the floating body were spherical; 
but it frequently happens that the wave does not bear them back, 
because they are wider or narrower in one direction than in the other, 
and being thus irregular in shape they are struck upon the side that is 
largest by another reflex wave which proceeds to roll over and over this 
movable thing which moves wherever it is carried, its movement being 
sometimes swift and sometimes slow, and turning sometimes to right 
and sometimes to left, at one instant upwards at another downwards, 
turning over and turning back upon itself, now in one direction and now 
in another, obeying all the forces that have power to move it, and in the 
struggles carried on by these moving forces going always as the booty 
of the victor. c 93 r. 


There can be no flow and ebb unless several rivers discharge them- 
selves in the same expanse of water. 

^ G95r. 

In the course of the year the amount of the water that rises will be 
as great as of that which descends in the rivers and the air. 

° H 29 V. 

[Course of river 

All the things which are lighter than sand will be left in the lower 
part of the river underneath the beginning of the fall of the wave. 

Where the water has least movement the surface of the bottom will be 
of the finest mud or sand. 

Where the course of turbid water meanders among the gnarled 
roots of thickets it will deposit much sand or mud through the many 
twists of its eddies. 


The water which gives less weight to its course is swifter. 

The water which is swifter drives its wheel faster. 

That gives less weight to its course which is straighter. 

The water of the mills ought to strike the blades of the wheels at 
right angles. 

That water which flows with less slant will strike the wheel farther 
from the perpendicular of its fall. 

That water which strikes farther from the perpendicular of its fall 
gives a less blow. ^ 

The wave created by the percussion of water upon the bed of a river 
will make a movement from below contrary to that from above. 

The wave is slower at the end of its elevation than at any other 

The parts of the wave which move most swiftly will be near the end 
of its fall. 

The sand remains higher underneath the highest part of the wave 
than under its lower part. h 31 r 

When a stone is thrown into still water it will create ripples that 
expand equally if the water is of uniform depth. 

If two stones are thrown one near to the other within the space of a 


braccio, the circles of the water will increase equally one within the other 
without the one destroying the other. 

But if the bottom is not level the circles will not expand in uniform 
movement except on the surface. 

When an object of long shape is thrown into water it will create an 
oval undulation. 

A round object thrown into running water will create an oval 
undulation in two movements. h 31 v 

Where the water is higher it has more weight upon its bed and its 
course is more undulating. 

That part of the bed or of the bank which projects with the sharpest 
angles into the straight course of the waters suffers most damage in the 
flow of the water. 

Water which strikes on an angle deepens the former sides. ^ ^ 

Every part of the surface of the water desires to be situated at an 
equal distance from the centre of the elements, and if one part of the 
surface be raised above another this so happens because of the contrary 
movements which are taking place between it and the bottom. ^ ^ 

Where the current is in the centre of the full stream the ridge will 
not be between the point of union of the eddies and of where the water 
rebounds; it is all deep. 

The large pebbles remain in the deepest part of the current. 

Where the channel of the water grows narrower it digs its bed 
deeper and flows more swiftly. H38 r 

Iron which receives continually the impact of flowing water never 

rusts but is consumed by beine burnished. 

, ■ H 39 r- 

In proportion as the object dividing the water is more distant from 
the surface it leaves less sand behind it. 

H 39 V. 

Where one body of water joins another at a sharp angle it will make 
a great depth. 


H 40 V. 

[Of things carried by the ns)ater'\ 

Where the water makes less movement there when laden it deposits 
its weight. ^ 

H 46 V. 

^ If a long object uniform in weight and thickness finds itself in the 
middle of an even descent, its length will move according to the length 
of the course of the water. 

When a long object moves in a channel midway between the middle 
and the contact of the bank it will move slantwise. 

The long object which is nearer to the side than to the centre will 
proceed to revolve upon the water. 


Where water has less movement there it deposits its weight more 

The eddies of water after it has struck the ground at an angle turn in 
contrary movement. 

H 47 V. 

Water will be in perpetual movement if its surface is not equidistant 
from the centre of the earth. 

Sand and other light objects follow and obey the twists and turns of 
the eddies of the water while the large stones move in a straight line. 

H 50 [2] r. 

Water which falls into smooth water causes it to become slanting, 
consequently its descent becomes swifter. 

H 50 [2] V. 

Measure the height of the falling water and multiply it by the height 
to which you wish to raise it, and as many times as the extent of the fall 
of the water enters into the height to which it has been raised, so many 
times is it thinner than that which rises; and this is the last and greatest 
amount that can be raised. , ^ 

Water which rises continually because of the movement of other 
water will be so much the thinner as that which moves it is of greater 

'“S'*’- HjaWr. 

Turbid water does more harm to the banks than clear water, and 
more at the base than at the top, because it is heavier and thicker. 

H 52 [4J V. 



The line of the water which has the greater movement breaks that 
of the lesser movement and buries itself beneath it. 

That part of the sand which is nearest to the impact of the falling 
water will be finer than the rest. 

The large shingle will be farthest away from the blow. „ 53 [5] r. 

I ask whether the water which emerges underneath comes from the 
surface or no. 

The first depth will be where the sum of the blow of the second 
water makes its way into the course of the eddies; the lesser where the 
second base is, is where the revolving water encounters it in its course. 

H 53 [5] V. 

After the descent of water that which was above remains below; the 
lower part becomes changed into the upper part. 

After the most rapid descent of the water the lower part remains of 
more rapid movement than the upper part. ^ 

Of waters that flow upon beds of equal slant that will have the less 
depth which has the greater breadth. 

Of waters that flow between banks of equal breadth that will have 
less depth which possesses the more rapid course. ^ ^ 

Water in its movement drags with it the air which borders on it. 

And the bed offers more resistance: this is why it moves more on the 
surface than at the bottom. 

All the upper part of the water which finds itself at the beginning of 

its fall will be lower than the other after this fall. r n 

H 55 [7] r. 

Water which flows in falls of equal slant will move more strongly at 
the bottom of the canal than at its surface. . tot 

H 56 [8] V. 

Waters which fall from the same level with an equal slant in an equal 
length of movement will be of equal swiftness. or v 

° H 58 [10] V. 

Of waters which fall from the same level by channels of equal slant, 
that will have the swifter course which has the greater length. 

Of waters which fall the same distance from the same level, that 
will be slower which is longer. h 59 [n] r. 



The percussion of the water upon the wheel will be at the highest 
degree of its power when it strikes within equal angles. 

The percussion made between equal angles will be of the greatest 
power when the current of the water and the movement of the wheel 
are in the same direction. , , , 

H 63 [is]r. 

The sand moved by two light currents of water settles itself upon the 
steep bank in a square ridge. 

Water which has struck against a round body will create equal 
hollows beyond the sides of this body. 

Gravel dug up by the blows of the water will settle where the move- 
ments made by the blows meet. 

That face of the triangle whichisinterposed between more nearly equal 

angles in the course of the water will be the cause of a great hollow in 

the water that strikes there. . r 

H 64 [163 r. 

Water which moves by a uniform slant will be swifter at the surface 
than at the bottom. 

The wave that is caused by a blow will be higher at the beginning 
than in the middle. 

Waves that are caused by the wind will be higher in the middle 
than at the beginning; that is the fourth [will be higher] than the 
third. ^ r T 

H 67 [19] V. 

These back-currents eat away the banks of the canals; you will there- 
fore make screens of wood to extend for the whole of their impact. 

H 68 [20] r. 

[Movement of water\ 

Water which exceeds the general depth and breadth of rivers moves 
in contrary movement. 

The wave of the water will swell between the cause of the movement 
and its end. 

Water which moves by reason of the undulation of the wind will 
make a contrary movement at the bottom to that at the surface. 

Water does not weigh less crosswise than in the line of its per- 

Every movement of liquid weighs more in the direction in which 


through a hole of equal size its vase empties itself more rapidly; the 
centre of the bottom of the vase receives a greater weight of water than 
any other place. h68[2o3v. 

The free movement made by the upper part of water will not make 
angles of any kind except in the percussion. 

All the upper lines made by the movement of water are curved. 
The wave follows the movement of the air which touches it. 

The object enclosed between the air and the wave does not follow 
the movement of the one or the other. 

The water that is expelled from the spot which the vessel occupies 
weighs as much as all the remainder of the ship which displaces it, 

H 69 [21] r. 

Streams of water equal in current and angle of descent which move 
one against the other, penetrate and pass through each other without 
turning aside from their natural course. h69[2i]v 

Water which moves against motionless water attacks and destroys its 

The water with the greater movement penetrates and traverses the 
lesser movement of other water, like air, . _ 

. H 70 [22J r. 

The line made by the course of water after its percussion leaps back 
at equal angles. ^ ^ 

The farther water is away from its bed the freer will it be in its 
natural movement. 

H 72 [24] r. 

Where the water has a stronger current the shingle is larger. Ail 
the detached shingle will turn its largest side slantwise against the course 
of the water. ^ 

H 74 [26] V. 

All light things gather together in the centre of the eddies that is at 

the bottom. v 

H 75 [27] r. 

Every portion of water desires its parts to be as the whole element, 
equally distant from its centre. 

^ ^ H 76 [28] r. 



The water which flows near the bed of the stream between the banks 
will be slower than the rest because of the percussions made by the 


[Error as to buying water\ 

You who buy water by the ounce know that you may greatly deceive 
yourselves. In fact if you take an ounce in stagnant water and an ounce in 
flowing water, against the hole of your ounce, an ounce near the surface, 
one near the bottom, one across the current ... 

In proportion as the natural movement separates itself from its cause 
so it becomes more rapid. or v 

^ H 78 [30] r. 

That wheel of the water will be better turned when the water that 
turns it does not leap back after its percussion. 

The blow will be of the greatest force when the movement which 
causes it is straighter and longer. h79[3i]v 

[Sand and water] 

All the hollows of the furrows visible in the sand will be between 
equal angles, according to the movement of the water, ^ r ^-i j. 

o F s A N D 

The wave is less sloping and of slower movement in its rise than in its 


The surface of the water of rivers desires to be equidistant from the 
centre; as it leaps it weighs down and consumes the bed because it 
grows thicker in the course of its intersections and increases in weight as 
it enters the air, and in consequence falls and bursts through the bed. 

H 81 [33] V. and 82 [34] r. 

In water that has no movement the leaves that ranged through every 
part of the water rest upon its bed. ^ 

The back-currents which are formed in the midst of the expanse 
of the falling water are situated between the leap of the water and 
its banks. „ 82 [34] r. 

The back-currents made by the water after the expanse of its fall will 

■ ' ■ ■■ 73 . . , 

be between the surface and the bottom, between the upper and the lower 


If the beds of two canals are of equal slant and breadth, and contain 
an equal volume of water, and one is restricted to two thirds of its breadth 
in the middle of its course and the other is uniform in breadth, I ask 
which will discharge more water. 

Water that falls into other water strikes against its bed and raises 
itself farther in the air than does the general surface, and then falls back 
and lessens its bounds. « s, v 

The lines of the water as it leaps after its percussion will not be in a 

straight course but will bend in a curve. 

H 84 [36] r. 

A straight canal of uniform depth and slant will make within a short 
time a deeper hollow in its centre than near the bank. 

The water in the middle of straight canals flows more rapidly than it 
does at the sides. 

Where the water has more movement it is lighter if it is of the same 

Water which has been pent up will burst the bank and the bottom 
after its fall. o r 

Every canal of water of uniform declivity, depth and breadth, which 
is pent up for a certain space, will burst its bed and its bank after the 
passage of this restricted area. 

This is due to the fact that where water is pent up it rises behind this 
barrier and after passing through this narrow place it presses on furiously; 
as it descends it comes upon the water below which does not flow and 
so it receives a check. After this it follows the line of its descent and 
goes to the bottom and burrows there and turns with a circular movement 
towards the banks, and hollowing these out from below it makes them 
fall in ruin, as is shown in the drawing above. ' , ' 

^ H 85 [37]r. 

\JVith drawingl 

Water below obeys its natural course less than that above. 

This comes about because the water that borders on the air is not 
made heavy by any weight, so that simply and without any restraint it 
obeys its natural course r 



That below is weighted and pressed and acts as is shown at a b. See 
that as it forms an angle at a and above at c it cannot form anything but a 

curved line. ^ r r, • 

All the waters some distance below the surface intersect after their 

percussion. h85[37]v. 

That water will turn in contrary course which exceeds the general 
breadth and depth of the rivers. 

Waters of equal breadth and unequal depth will be of equal move- 
ment on the surface. i . i • -u 

Among the currents of water of equal slant that which is the 

straightest will be the swiftest. h 8y [^9] r. 

Water which exceeds in depth or breadth the general breadth and 
depth of the river will turn against its first course. ^ 

I Method] 1 ^ r 

Remember when discoursing about water to adduce first experience 

and then reason. h 90 [42] r. 

Of streams of water equal in length, breadth and declivity, the swiftest 
will be the one of greatest depth. h 92 [44] v. 

All the movements of streams of water which are equal in dep* and 
declivity will be more swift at the surface than at the bottom, and more 
at the centre than at the sides. h 93 [45] r. 

Water, which is the vital humour of the terrestrial machine, moves by 
its own natural heat. h 95 [47 v.] r. 

I The circulation of water] • -u 

The water which from the lowest depths of the sea entering by the 
force of its mover is driven to the high summits of the mountains, there 
the severed veins, hurls itself headlong and returns by *e shortest 
way to the depths of the sea; and again it raises itself through the rami- 
fication of its veins and again falls back, and thus, coming and goin^ 
sometimes high and sometimes low, inwards and outwards, it 
with natural or accidental movement after the manner of a screw, whi 



the water that is poured away through its severed branches and falls back 
upon itself rises again through its courses and returns to the same points 
of descent. Hioi [+2r.]v. 

Where three currents of water meet together there will be created a 
sudden depth, for they rise and acquire weight and then movement 
with force, and this breaks in the percussion that it makes upon the 
bottom. , 

\OJ the fall of a mer\ 

If the bottom of the bed of the river from which the water hurls itself 
is hollow in the centre, the water which moves from the sides and directs 
itself towards this centre will raise itself before falling. 

If the river as it flows strikes against some rock, it will leap up, and 
the place that it strikes in its fall will be of the nature of a well. 

I 62 [14] r. 

If the rock in a river projects above and divides the course of the 
water which rejoins after this rock, the interval that is found to exist 
between the rock and the reunion of the water will be the place where the 
sand becomes deposited. 

But if the rock that divides the course of the waters is covered by the 
flowing waters only in its lower parts, the water that passes above will 
fall behind it and form a hollow at its feet and cause it to turn ; and the water 
that falls headlong into this chasm turns in vortex upwards and down- 
wards, for the uniting of the two streams of water which had been 
divided by the rock does not suffer the water immediately to pursue its 

X 67[i9]v. 

Every natural and continuous movement desires to preserve its 
course on the line of its inception, that is however its locality varies it 
proceeds according to its beginning. 

This movement aforesaid occurs in the course of rivers, which always 
attack and destroy whatever opposes the direct line of their course. 

But if these rivers were straight, with equal breadth, depth and slant, 
you would find that with each degree of movement they would acquire 
degrees of speed. 

Consequently if there is a change or diflPerence in their slant there 


is a difference in their course; and where there is less inequality in 
breadth they become deeper; and given an equal slant, where they are 
wider they become slower. Therefore the waters which desire a 
straight course, and to make themselves swifter at each stage of 
movement, finding the places through which they pass wider and 
deeper become slower and break the bed or the bank. r 

^ I 68 [ 20 ] r. 


The movement of the rebound of water is swifter than that of the 
percussion when the water that strikes is much mingled with the air. 

I 68 [ 20 ] V. 

For the air is capable of being compressed, and the more it is 
pressed the more it has weight within the other air; and the greater its 
weight the greater its percussion against its object, as is seen with 
winds which are constrained from great breadth to pass through a narrow 
defile of the mountains: if there were no opening above them they would 
not fill up the spaces of the things in front of them, but they are able to 
expand above with great facility because there are great spaces between 
the hills . . . and below readily, and the wind flies easily towards the height. 
Remember how Augustus made a vow in Gaul to the wind Cirrius 
because for just such an impetus he had to lose his army, and there he 
made a temple. r i ^ r n j 

i I 68 [20J V., 69 [21] r. and V. 

Water will leap up far higher than it has fallen, through the 
movement caused by the air which finds itself shut in within the bubbles 
of the water, and which afterwards rises and floats like bells upon the 
surface of the water. Returning to the place where it strikes, the water 
is again submerged by the blow, so that the air finds itself hemmed in 
between the water which drives it down and that which encounters it, 
and being pressed upon with such fury and violence suddenly 
through the water which serves it as a covering, and like a thunderbolt 
emerging from the clouds so this air emerges from the water carrying 
with it a part of the water^ which previously formed its covering. 

[Water in canals\ ^ ^ ^ 

When water in some part of its passage through a narrow canal 
becomes wider it immediately becomes shallow and swifter because it 
1 MS. has air. 

. , , 77 . V.",,. : ' 


finds a slope where it moves vigorously. And along the course it has 
commenced it directs itself to the foot of its dike and strikes it. 

After which percussion it turns upwards and proceeds with a whirling 
movement hollowing out the foundation of the bank until it returns 
upwards. And this process of hollowing it out gives it the shape of the 
hull of a ship, narrow at the commencement and the end and in the 
centre deep and wide, ^ r. 


Here arise the bubblings or wellings up of water in the middle of 
the higher eddies. And it may be asked whether the movement of the 
eddies starts because it runs towards the percussion of the water, which 
is lower than in any other adjacent part; or because the thrust of the 
water that flows in the centre of the breadth of the surface is that which 
as it strikes the other waters raises them and makes a hill with the other 
water, and then returns towards its entry in the expanse of water; or if 
the water struck by the other waters in its stream and pressed by it 
gushes up and leaps back to the place from which the current comes. 

I 71 [23] r. 


The name pelago (sea, large lake) is applied to an area large and 
deep in form in which the waters lie with little movement. Gorgo 
(whirlpool) is of the same nature as the pelago except for a certain 
difference, and this is that the waters that enter into the pelago do so 
without percussions while those of the gorgo are made up of great 
falls and bubblings up and surgings occasioned by the continuous 
revolutions of the waters. Fiume (river) is that which occupies the 
site of the lowest part of the valleys and which flows continuously. A 
torrent is that which flows only with rains: it also makes its way in the 
low parts of the valleys and joins itself to the rivers. 

Canal is the term applied to waters regulated within their banks by 
human aid. Fonfi (sources) is the name given to the birthplaces of 
rivers. Argine (bank) is that which with its abrupt height withstands 
the widening of rivers canals and torrents. The rip a (bank) is higher 
than the argine. The riva (shore) is lower than the argine. The spiaggia 
(beach) is among the lowest of the parts which form boundaries with 
the waters. Lago (lake) is that in which the waters of the rivers assume 



great width. Paludi (marshes) are stagnant waters. Grotte (caves) are 
hollows formed in the banks of rivers by the course of the river; their 
length follows the line of the course of the water; they have some depth 
and also find their way under the foundations of the bank, losing their 
shape as they near the end of their course. Caverns are of the shape of 
ovens which enter far beneath the bank, and the waters in them are in a 
state of wild turmoil and are constantly increasing. 

Pozzi (wells) are the sudden depths of rivers. Stagm (pools) are the 
places of refuge for the waters of floods or storms, their beds being firm 
and thick so that the soil can neither drink in nor dry up these waters. 
Baratri (chasms) are also places where the water suddenly becomes deep. 
Procelle (storms) are tempests of Polulamenti e surgimenti 

(bubblings and wellings up) are the beginnings of the waters; but the 
former come from below upwards and the latter merely in transverse move- 
ment which falls from some grotto. Sommer gere (submersion) is under- 
stood to refer to things which enter under the water; inter segatione 
dacque (intersection of waters) takes place when one river cuts the other. ^ 

172 [24] r. and v. 

When the general courses of the rivers are contracted, as they issue 
from the valleys and enter amid the defiles of the mountains, the water 
will heap itself up in its wide part; and it will make great descent and 
movement through the said contracting of the mountains, and after 
passing the middle of this contracted part it will make a great hollow, 
and then having entered again in the broad part it will lack depth, in 
just such proportion as the wide part increases in such a way that the 
waters become of equal course. 

And the said depth will be lacking after the leap of the waters, be- 
cause it will become filled up with shingle beneath the greater altitude 
of the leap of the said waters. 

If the fall is of the same width as the river, the water that strikes the 
bottom will leap up and then fall back again by each line that departs 
from the centre of the surging mass, and the farther they descend from 
this surging mass the more they spread out. And part is moved by the 
course of the stream, and as a consequence it is necessary for it to make 
three movements, each of which consumes a considerable portion of the 
foot of the bank. 

^ A list of words is added, descriptive of movement of water. 


For that which descends from the summit of the surging mass throws 
itself towards the bottom, and since such descent is slanting it acquires a 
movement towards the bottom of the bank; and as this descent follows 
in part the general movement of the river, this surging mass falls with a 
threefold descending movement, one proceeding downwards, another to- 
wards the bank, another towards the course of the river. And all three 
consume the base of the bank, by reason of the great displacement 
occasioned by so much impetus; for if the river were to flow for a long 
way hugging the bank it would be able to find some stone which at some 
spot would protect a piece of this bank near to it; but this movement 
proceeds downward towards the bottom, forward towards the bank, 
downward towards the course of the stream, in such a way that each 
stone is struck by three different movements and on three different 

From which it follows that if the soil is friable it crumbles away 
in a short time. _ „ [a 6 ] v., 75 [n] r. 

\Of the movement of water — bubble s\ 

When one sees mountains rising in the running waters, rising in the 
form of bubbles, it serves as a sign of the great depth from which these 
bubbles spring after the percussion made by the water upon the bottom; 
and by the speed of its rebound it bores through and penetrates the other 
water and then turns towards the surface of the running water and passes 
through it, rising up in this way; thereafter acquiring weight it loses its 
first impetus and falls down again by each line round its centre, and 
returns again towards its bed. i 6 fzSl v 


Of the difference water makes in its course if its sides strike on a 
strand, a bank, or other water, that is in passing by a piece of stagnant 
water or running water crosswise. 

One should also observe what differences there are in rivers if they 
fall upon beds of different natures, namely upon stone or earth, or tufa 
or clay, sand or mud, or stagnant or running water, and this crosswise 
or slanting or opposite, or by the same line as the water itself, that is by 
the line of the same current but slower or swifter than that which it 
strikes, or more level or more slanting. 

■ 8o ' 


O F E D D I E S 

One asks why the percussion of water within water makes lines of 
circular movements and eddies, and its leap is not straight as is that other 
which beats upon its shores and banks. 

Why bubbles are not continuous when the falls of the water are: 

The reason is that the water which flows above after falling is swifter 
than that which flows below; and when that below precipitates itself in 
some chasm It raises itself towards the surface with almost the same 
impetus, and sometimes subdues and overcomes the water that flows 
above and sometimes is subdued by it. 

Being thus in a state of equilibrium as to its power of movement some- 
times one conquers and sometimes the other. A V j 

^ I 77 [29] r. and v. 

Things lighter than water do not follow the course of the rebound 
and intersection of the water, but pass along the centre of its current or 
near the parts as they are found at the entrance of the currents, and are 
not impeded unless by equal pressure, because if the right wave of the 
rebound meets with the left, it is necessary, if they are of equal power, 
that the place of their percussion be thrown back equally. 

Consequently things in this place which move upon the water, not 
being driven more by one percussion than by the other remain in the 
same line of current. But if one of the forces of the wave be greater than 
the other, that is by the -swiftness of its current, I do not mean force 
arising from a greater quantity of water, for if the one water was much 
less thick than the other this would not matter: for let us suppose one 
body of water to be less than double the other in volume and to 
acquire double its speed; now since these bodies of water clashing 
together are of equal size in their contact, as I have proved in the third of 
the fifth, the larger being a square braccio and the lesser of a half braccio, 
the lesser does not strike the greater unless it is in its half, and in the same 
way the greater strikes the lesser with its half, so that the contacts made by 
the percussions are equal in quantity and unequal in that the power is 
double, the speed of the one being double that of the other. 

O F T H E E D D I E S 

Sometimes there are many eddies which have a great current of 
water in the middle of them, and the more they approach the end of the 
current the greater they are. These are created on the surface by the 


waters that turn back after the percussion that they make in the most 
rapid current, for the front portions of these waters, being themselves 
slow, on being struck by the swift movement, are suddenly transformed 
into the said speed. Consequently the water which touches them behind 
is attached and drawn by force, and torn away from the other, so that it 
turns all in succession, one (wave) following the other with a like swift- 
ness of movement, if it were not that such current at first cannot receive 
it so that at any rate it does not rise above it, and as this cannot be lt is 
necessary for it to turn back and consume in itself these swift movements. 
From that time the said eddies with various revolving movements pro- 
ceed to consume the impetus that has been begun. And they do not 
remain in the same positions, but after they have been formed thus, turn- 
ing, they are borne by the impetus of the water in the same shape, in 
which they come to make two movements; the one is made in itself by 
its own revolution, the other as it follows the course of the water which 
is carrying it along all the time that it is destroying it. 

I 78 [30] r. and V., 79 [31] r. 

[Air and njbater\ 

The water which by a slight movement encloses, a little way below 
its surface, the air which is submerged with it, turns with a slight impetus 
out of the surface, carrying with it such covering of water that being of 
equal weight with this air it stands above it in the form of a half-spherical 

But if this air is submerged with impetus it comes back out of the 
water with fury for the length of the movement made beneath the water; 
and pressed by its weight it leaps out of the water, breaks its surface with 
its impetus and flows on with straight course after the manner of wind 
emerging from bellows which discharges itself in a stream through the 
air; and therefore it does not, as does the former as it floats upon the 
water, remain enveloped in its surface. „ r . 

* I 80 [32] V. 

How all the air which leaps back with the water does not remain on 
the surface but by its impetus submerges itself anew amid the revolutions 
of the waters: 

How the movements of the waters among the other waters are 
not obliged to move more by a straight line than a curved one, and 
how after leaping back as they wished these waters are not obliged 
to be at rest, but in order to return to a low place and with a revolving 



movement they go attending the course of the river until they have 
discharged the air that is enclosed within them on the surface of the 
sheet of water. „ . , 

I 8i [33] r. 

[Of water f owing into water\ 

B E N D o F C U RR E N T 

If the entry of the water into the sheet of water (pelago) is of circular 
shape the concavity of its base will be of the form of a crescent, receiving 
the shingle within its circumference or within the two horns of this figure. 

I ask whether if the current should make some bend it will become 
hollow at the bottom or in the middle or above, and the same thing as 
regards the leaps which follow afterwards against the bank of the rivers, 
the bed being of uniform substance, and also as to the bank where it is 
raised, where it leans and the methods of effecting its repair. 

I 8i[33]v. 

[Of falling water\ 

I ask as to the shape that water assumes in the different slants of its 
descent in each of its falls, and what shape the concavity will have when 
the water strikes upon a bed of uniform substance; and I ask as to the 
shape the shingle will take which is left after the percussion of each of 
these, and the remedies when they are injured. ^ 82 [34] r 


Because the straighter the river the swifter will its course be, and the 
more vigorously will it gnaw and consume the bank and its bed, it is 
therefore necessary either to enlarge these rivers considerably or to send 
them through many twistings and turnings or to divide them into a 
number of branches. 

And if the river through many twistings and turnings becomes slow 
and marshy through its many detours you ought then to straighten it, in 
such a way that the waters acquire sufficient movement and do not cause 
destruction to the banks or dikes; and if there should be depth near to 
some dike you ought to fill up the spot with gabions together with 
fascines and shingle, so that it may not become hollowed out by move- 
ment under the dike, and so by causing it to crumble the river may 
afterwards proceed to make a bend in your land or villa and there 
straighten its course. i 82 [34] v. 


\0f the earth carried by water\ 

When the water in the floods commences to find a place where it 
can flow, it begins with its feeble inundation to strip and carry away the 
lightest things, and deposits them where its course becomes feeble, then 
as it grows it carries away the heavier things such as sand, and carries 
them over the former things and there leaves them, and even though the 
water should not increase, by the mere fact of its continuance it proceeds 
by degrees to carry away the things from the place where it flows; but by 
reason of their weight it cannot carry them so far forward as the first 
lighter things, and if it then carries away the heavier things it deposits 
them proportionately near to the spot from whence it took them. 

How to restore the soil to the places that have been uncovered and 
stripped bare by the courses of the waters on a hill or mountain or in 
sandy places. 

For the rains, or to provide an outlet for other waters, one ought to 
construct canals or mouths of rivers, for the places where they pass in 
so great current that they tend to become turbid by reason of the earth 
they carry with them and to be changed; then when they are at the 
place where you wish that they rid themselves of the soil, these canals 
of water are divided into many small channels of water, after the manner 
of furrows, and their violence is lessened and they grow clear again. 

I 83 [35] r. 

\Qf flowing water'\ 

Where the river is constricted, it will have its bed stripped bare of 
earth, and the stones or tufa will remain uncovered by the soil. 

Where the river widens, the small stones and the sand will be 

Where the river widens considerably, there will be discharged the 
mud or the ooze and bits of timber and other light things. 

Where several currents of water run together, there will instantly be 
formed a hollow that will be navigable. 

Where the waters separate, the sand and ooze will be deposited and 
the bed will be raised in the shape of the half of a ship inverted. 

Beneath the rebounds of the water, there will be formed hills of sand 
or stones. 

Beneath the repercussions, that which rests under the rebound will 
become raised. 



Where the water finds the place higher, which forms an obstacle 
beneath it, it makes a greater and higher wave and then forms a deeper 
hollow. ■ , 

I 83[35]v. 

Where you find much sand you will find at the end of it in front or 
behind shingle or bare tufa. 

Sand is discharged when waters meet in their course, for in such a 
spot nothing can remain that offers resistance to a current so reinforced; 
light waves drop their sand at the sides of the said current, and the sand 
as the current becomes less swift forms a cover to the shingle. 

Sometimes the lesser floods carry branches covered with leaves from 
the plains and deposit them in their small movements, and then, becom- 
ing stronger, heap sand upon the edges of these branches and still 
increasing carry there shingle and tall large stones. 

\The rebounds of water\ 

The rebounds that water makes which rise through the percussion 
of water which has fallen upon other water, are not carried between the 
equal angles of its percussion, but will leap to the surface by the shortest 
way, through the air that was submerged together with the water. 

I 84[36]v. 

If a stone is thrown into still water it will form circles equidistant 

from their centre; but if into a moving river the circles formed will 

lengthen out and be almost oval in shape, and will travel on together 

with their centre away from the spot where it was first made, following 

the course of the Fstreaml ... nr-, 

I 87 [39] r. 

O F W A V E S 

The waves are of [twelve] kinds, of which the first is made in the 
upper parts of the waters; the second is made above and below by the 
same path; the third is made above and below by contrary paths, and is 
not in the centre; the fourth is made so that from its centre upwards it 
runs in one direction and from this centre downwards it makes the 
opposite movement; the fifth flows downwards and not upwards; the 
sixth flows downwards and above has a contrary movement; the seventh 
is that of the submersions of waters by means of a spring that enters into 
the earth; the eighth is that of the submersions by means of eddies which 
are narrow above and wide below; the ninth is that of the eddies wide at 

85 \ . 


the surface and narrow at the base; the tenth is of cylindrical eddies; the 
eleventh of eddies that bend in regular curves^; the twelfth is of the 
slanting eddies. Make here all the waves together, and all the move- 
ments by themselves, and all the eddies by themselves. Arrange thus the 
series in order separated one from the other. And so also the rebounds 
of how many kinds they are in themselves and also the falls. And set 
down the differences that there are in turbid waters, in their movements 
and percussions, and those that are clear; and similarly in waters that are 
violent and those that are sluggish; in those that are swollen and those 
that are shallow; and between the fury of pent-up rivers and those with 
a wide course; and of those that run over great stones or small ones or 
sand or tufa; and of those that fall from a height striking upon different 
stones with various leaps and bounds, and of those that fall by a straight 
path touching and resting upon a level bed; and of those that fall from 
a great height alone through the air; and of those that fall through the 
air in shapes that are round or thin or wide or separated or united. And 
then write down the natures of all the percussions: on the surface, in the 
centre, and at the bottom, and of their different slants, and the different 
natures of the objects and different shapes of the objects. 

And if you give movement to a sheet of water, whether by opening 
its sluices above, or in the middle, or below, show the differences that are 
caused by it falling or moving on the surface, and what effect it makes 
in entering with such fall upon the ground or in stagnant water, and 
how that by which it is moved at first maintains itself in a channel level 
or uneven, and how it produces all at once eddies and their recesses, as 
one sees in the basins of Milan, and the nature of the sudden rush of the 
rivers, and so also with those that grow little by little; of the waters 
also that cannot in the great floods pass through the arches of 
the bridges which surmount them, and how the water that passes 
through these arches increases the impetus through having a great 
weight above. ■ ■ , r n 

° I 87 [39] V., 88 [40] r. and V. 

\The water of mills\ 

I ask whether if the impetus of the waters that turn the mills creates 
a protuberance either across above or below near the place of percussion, 
this percussion will have the same force as if this water ran in a straight 

I 89 [41] r. 

^ MS. dequal nacuita 


O F W A T E R 

Rivers when straight flow with a much greater impetus in the centre 
of their breadth than they do at their sides. 

When the water has struck on the sides of rivers with equal percussion, 
if it find a part of the river narrower it will leap towards the middle of 
the river and these waves will make a new percussion between themselves; 
as a consequence they will return again towards the banks, equally, and 
that water of conical shape, which is enclosed between the first per- 
cussion made upon the bank and the second made in the centre of the 
stream, will slacken at its base and be swift near to its crest. Striking the 
bottom they will afterwards rise equally to the height of the intersection; 
but always that of the centre will be swifter than that which leaps back. 

Water which moves along an equal breadth of river and on an equal 
bed will have as many different thicknesses as there are different slants 
in the bed where it runs; and by as much as it is swifter in one place than 
another so proportionately it will be more shallow. 

1 105 [57] V., 106 [58] r. 

O F M O V E M E N T 

Water which falls from the height of a fathom will never return to 
the same height except in small drops, which will leap much higher 
because the motion of leaping back will be much more rapid than that 
of the descents. In fact when the water falls it buries with it a great 
quantity of air, and after the (other) water has been struck it leaps back 
towards its surface with a force which creates a movement almost as rapid 
as was that of the descent; but not actually so for the reason given in the 
second of the seventh, where it is stated that the movement of the rebound 
will never be so swift as was the descent of the substance which rebounds; 
or thus: — a succeeding rebound will never be equal to that which pre- 
cedes it. So that in consequence the rebound which the water makes 
proceeds from the base where it has been created, almost with the speed 
of the descent that has given it birth; and in addition to this there is added 
to it a second momentum which augments this motion, namely that of 
the air that is submerged by the fall of the water. This air clothed 
around with water bounds up with fury and leaps into its element like 
wind driven by the bellows; it carries with it the last of the water which 
is close to the surface, and by such an increase causes it to leap up much 
farther than its nature demanded. i 108 [60] v., 109 [61] r. 



The farther the circular wave is removed from its cause the slower 

will it become. 

I 1 14 [66] r. 

\The meeting of mater-courses\ 

If the courses of two lines of water which cross each other in the middle 
or in a part of their river-beds pass either the one into the other or the 
one over the other, do they then each leap back after the percussion? 
Certainly they leap, because it is impossible for the two bodies to pass 
one through the other. 

But after the two bodies have clashed together they will widen 
themselves at their point of contact, and after having struck they will 
recoil to an equal distance from the centre of the percussion. And 
that body which goes upwards follows its nature, and the other body 
below the centre of the impact which would wish to go downwards 
and cannot, increases that above. 

’ T I lA 06 V. 


Make one side of the channel of glass and the remainder of wood; 
and let the water that strikes there have millet or fragments of papyrus 
mixed in it, so that one can see the course of the water better from their 
movements. And when you have made the experiment of these re- 
bounds fill the bed with sand mixed with small shingle; then smooth this 
bed and make the water rebound upon it; and watch where it rises and 
where it settles down. 

Then make the bank on the wooden side of mud, and watch its effects 
through the glass, and make it again in flowing water. ^ ^ 

[Movements of water^ 

If the water was a quantity endowed with sensed as it is a continuous 
one, the movement that it makes between the extreme elevations and 
depressions of its waves would be unequal. 

In effect the part that rises acquires degrees of slowness in each 
degree of movement, in such a way that at its greatest elevation it is 
in the extreme stage of slowness. 

And afterwards in descending it acquires degrees of speed in every 
degree of movement, so that at its lowest depth it acquires greater 
^ MS. disscreta 


movement; therefore the resistance that ends its descent is that which 
receives the hurt, and that which ends the height of its elevation has no 

But if the quantity is continuous: the continuous quantity has equal 
movements when its river is of equal size and depth, because being all 
united together it is necessary that in all the parts of its movement each 
part draws and is drawn, pushes and is pushed, or drives and is driven. 
And it is necessary that this be with equal movement and power; and if 
it were not so the water would multiply more where it was slowest and 
would fail where it had most movement. . 

1115 [67] V., 116 [68] r. 

Where the water divides it rises; and afterwards as it falls down again 
it strengthens its course by the increased descent that follows. 

Where the waters join they rise; and then the near movement that 
follows becomes slow. . 

I 1 16 [68] 

When in the courses of rivers there are two currents of water, com- 
mencing the one far from the other, which meet in a place where they clash 
together, they will rise up after this percussion, and their bed will be but 
little consumed because they depart from it; and afterwards they will 
fall back again as they separate, and fall asunder, and falling back again 
they will strike and scrape upon their bed. By reason then of this percussion, 
which beats and scrapes the bed with its movement, a depth will be pro- 
duced there; and this happens in the great currents of rivers. 

1 117 [69] r. 

\T he height and depth of the wanjesl 

O F T H E S U M M I T O F T H E W A V E S 

The greatest elevation of the waves will not wear away its bed be- 
neath itself; in effect it touches it but little, by the fifth of the sixth which 
says that everything weighs by the line of its movement; from which we 
may say that this wave moves towards the air that flies from its per- 
cussion and weighs towards the air. If however the amount of friction 
is slight, it will ’ have but little force and will consume the bed but 


Whatever obstacle forms the chief cause in breaking the straight 
course of the water will be most consumed and displaced by it. 



Therefore we may say that if the air were the cause why the straight- 
ness of the elevation of the wave is broken it would be consumed by this 
percussion of water. But this air is not the cause of the breaking of such 
a course; the only cause of it is the force which the water acquires as it 
emerges from its element. And it would relax its pace in such a position 
if it were a sensitive quantity, but being as it is a continuous quantity 
it is necessary that one body of water pushes and the other draws, because 
they are united. ^ 

If the water moves more swiftly in the falling of the wave than in its 
rising, and at what point this water delays most. 

The water that moves in the formation of the waves will find itself 
of as great speed during its ascent as that of its descent, and it will have 
as much in the middle of its lowest depth as that of its greatest height. 
And if it was not of equal movement it would not be of equal depth or 
breadth; and if however it was of equal length and depth but not of 
equal movement it would form a great height in the place where it 
slackened most. „ ^ ^ 

The water flows more strongly at the sides of a covered rock than 
above it and after it has passed it, and for this reason it twists the 
waves made by its rebounds, producing on its surface crescent-shaped 

. r.3.[75]r, 

\The different sorts of rebounds of nsoater^ 

The rebounds of the waters are of two kinds, that is they are formed 
from two causes; one is that of the lumps of the bed on which the water 
passes, the other is when the parts of the water that strike against the 
lumpy parts of the bank leap back to the opposite bank. These masses 
of water on striking leap back to the opposite bank and press and drive 
themselves upon the first wave that they meet, and swelling leap 
towards the sky; and each flies equally from the place where it has 
struck, until another wave drives it back and afterwards another drives 
it forward. 

So in succession they fill the surface of the rivers with a trellis pat- 
tern, always raising themselves to the positions of the above-mentioned 

I 127 [79] V. 


[Ru/e as to rebounds: experiment^ 

I ask concerning the rebound: if the first rebound is ten braccia tell 
me how far will the second be. Dye the ball so that it marks the spot 
where it strikes upon the marble or other hard substance, study the 
position of each of the rebounds in succession, and so deduce the rule. 

I 128 [80] r. 

If you throw sawdust down into a running stream, you will be able 
to observe where the water turned upside down after striking against 
the banks throws this sawdust back towards the centre of the stream, and 
also the revolutions of the water and where other water either joins it or 
separates from it; and many other things. 

W A T E R A N D N A T U R E 

Water is nature’s carter, it transforms the soil and carries to ... a 
great part ... double. ^ ^ ^ 


Simple movement: Many rivers there are that increase their waters 
at every state of movement without loss. 

Simple movement: Many there are that lose without ever acquiring. 

Composite movement: And there are a considerable number which 
acquire more than they lose. 

Composite movement: And a considerable number lose more than 
they acquire. 

I have written in how many ways water hollows out the bottom, and 
in how many ways it deposits earth upon the bottom. And the same of 
the banks: where it raises them and where it forms them, and in how 
many ways it hollows out the soil of the banks, and the estates where 
during its floods it goes spreading itself beyond its banks. ^ ^ . g. 

The eddies of water are always produced in the middle water. 

The middle water is that above the mouth of the water which is bent 
across near to where it runs into the canal. 

The middle water is that between the water that is falling and that 
which is thrown back. _ . 



Should two streams of water encounter each other and then bend 
together in the same flight, the middle water will be found beyond this 
flight upon the current that has less power. 

The surface of the water which bends in leaving the straight line of 
its course for the lateral outlet will be always higher in the centre than 
« besides. K94[H]r. 

Of the water that is poured through a hole of uniform size situated 
at the bottom of its reservoir, the part that is nearest to the wall of this 
hole will have greater height and greater movement than the lateral part, 

K 94 [14] V. 

When water is poured in different streams from one reservoir into 
another that will be higher above its hole which is poured through a hole 
of less width, and the proportion of the height will be the same as that 
of the width of the holes. 


When two streams of water encounter each other and then pour 
through the same channel to the bed of a river, eddies are created there 
on the right hand and on the left, and sometimes these eddies of the right 
and left become reunited. . , 

K 96 [16] r. 

The water which moves in a river is either summoned or driven or 
moves of itself. If it is summoned or as one may say requisitioned what 
is it that requisitions it? If it is driven what is it that drives it? If it moves 
of itself this shows it to have a reasoning power; but in bodies which 
undergo continual change of shape it is impossible that there should be 
reasoning power, for in these bodies there is no judgment. 

K lOI [21] V. 


All the embankments of rivers against which the waters strike ought 
to be so much the more slanting as the percussion of the water is of greater 

Water rises higher upon the bank against which it strikes when it 
finds this bank more slanting; and consequently descends with greater 
impetus to strike against the opposite bank. 

K 102 [22] V. 

What difference there is between the percussion of the same quantity 
of water when it falls through the air or falls shut up in a conduit: 

92 ■ 


The water which falls in a perpendicular line becomes shrill at some 
stage of its descent. When it falls through a conduit this is left empty, 
and here the air fights with the water as will be said in its place. You 
should not forget however to say that this descent of the water is checked 
by the condensation of the air in the conduit where the water is. 

K 103 [23] V. 

If the waters that enter into a reservoir or issue forth from it have the 
holes of exit equal to the holes of entry, and the fall of the entry is longer 
than that of the exit, the entry will then be greater than the exit until the 
water of the basin rises, and then they will become equal. , ^ 

^ K 104 [24] r. 

And if the fall of the entry is more beneath the surface than the fall 
of the exit, although they are of the same size, the entry will be greater 
than the exit until their powers equalise themselves. 

But if in this case the exit covers a longer space of the surface than 
the entry does then the exit will be greater than the entry. ^ ^ ^ 

What shape will the same quantity of water moving along the same 
slant have in order that it may be as swift as possible? 

Let it have that which will make least contact with the bottom, that 
is a half-circle. 

That water will be swifter when the part that makes eddies through 
striking upon the bottom and the sides is less in bulk than the rest; and 
this is the greatest river. ^ ^ 

O K 105 [25] r. 

[Relation of wave and windl [Diagram\ 

The wave increases because the wind increases. 

D b ef the wind, strikes ef the water, and causes it to overflow; daec 
the second part of the same wind finds c e prepared to overflow, having 
come from ef and comes behind it with its power; and doubles the power 
t V e f and so makes the wave double. ^ r 

K 100 [26] V. 

Whether the percussion made by the water upon its object, is equal 
in power to the whole mass of the water that strikes when it finds itself 
in the air, or no. 

Which is the easier, to raise the sluice of the mill with the water 
flowing, up or down or across, or when the water is still. 


Vessels of equal capacity and full of water in double proportion and 
which empty themselves by holes made in their lowest depth, in each 
degree of time will change the degrees of proportions in the copiousness 
of their discharges. 

I maintain that if at the commencement of the discharge the water 
is of double quantity, the amount of the discharge is immediately double 
in the one case what it is in the other, varying immediately; in such a 
way that if the descents are divided in six stages in the lesser vessel and 
twelve in the larger one, when the lesser vessel has had a drop of five 
stages and the greater five also, this lesser vessel is left with one stage of 
height of water and the larger with seven, which is in proportion seven 
times as great. o r on 

® K 128 [48] r. 

\Fall of water\ 

Water which falls in the form of a pyramid by a perpendicular line 
upon a level surface will leap up again to a height and will end its point 
towards the base of this pyramid, and will then intersect and pass beyond 
it and fall down. 

L I r. 

[Air replacing njoater'\ 

Why the air which fills up the void in a globe from whence the water 
emerges, enters with the same impetus as that of the water which is 
poured out. Whatever is resting upon this water turns in contrary move- 
ment to that of the water. 

L 17 V. 


The long thing of uniform thickness swells as much in its two 
opposite sides as it is lowered in its two other opposite sides. 

Here the water which is confined in the parallel river increases as 
much in height as it is lacking in breadth; consequently as it falls it 
hollows out the place where it has struck. 

The parallel rivers may at some part of their length be confined in 
two ways, namely between their surface and their bed or upon their 
opposite sides. 

L 30 r. 

[Falls of V)ater\ 

When two streams of water meet at an extremely sharp angle the more 
powerful hollows out its side of the base most, and makes a sudden depth. 

94 ■ . 


This is the true way of giving the fall while conserving the bank to 
the water which descends from the said bank. 

L 3 I V. 

\The course of rivers'] 

The beds of the rivers uncovered naturally, do not give true indica- 
tions of the nature and quantity of the objects carried by the waters, 
because in the deep waters many places are filled with sand, and after- 
wards in the particular lateral courses of the rivers these deposits of sand 
are borne above the shingle on which they rested or laid bare beneath, so 
causing the continual subsidence of the raised bank of this sand which 
by reason of its lightness accompanies it in its course and is then deposited 
where the current of the water becomes more tranquil. 

The twistings of rivers in flood are such as to burst every dike and 
all the order that the river keeps when low. 

^ L 32 r. 

\F alls and courses of water] 

Water that has fallen with great impetus from its dam reproduces the 
twistings of the rivers according to the line of its fall, but when the waters 
subside, although the line a b keeps its place even if this river should 
swell again, the canal a b will become filled with sand, and the volume 
of the water will follow its natural course. 

L 32 V. 

\Water in percussion] 

When water strikes it rises, and it acquires weight in proportion as 
it leaps out of its common surface; this fallen back upon, the other water 
strikes it and penetrates as far as its bed, which it consumes perpetually; 
and such a hollow is formed in the length of the sides of the object struck. 

To guard against this a flat surface may be formed round any 
column which has a firm base and is of such breadth that the water that 

falls back is compelled to find it. 

^ 1-33 r- 

The less curved the bank where the leap of the river strikes it the 
farther removed will the second leap be from the spot from which the 
first departed. ^ 

s: L 26 V. 

The eddies of rivers are of several kinds; of these some are hollow 
in the centre after the manner of a concave pyramid; others full in the 


centre like a raised cone; some throw things up from the bottom, others 
submerge things borne on the surface of the water; and the one creates 
a hollow underneath the bank which forms its side, the other fills it up. 

These eddies serve the purpose by their revolutions and delays of 
equalising the excessive speed of the rivers; and as therefore the eddies 
at the side are not sufficient, by reason of the narrowness of the rivers, it 
becomes necessary that new kinds of eddies should be created which 
shall turn the water over from the surface to the bottom and at various 
different angles; of these some meet at the bottom and churn up all 
the soil which the eddy of the surface has in course of time deposited. 
And the other eddies do the same against the banks of the rivers. 

B.M. 30 V. 

A book of how to drive back armies by the fury of floods caused by 
the letting loose of waters. 

A book of how to inundate armies by closing the outlets of the 

A book to show how the waters bring down in safety logs hewn in 
the mountains. 

A book of how boats are forced against the rush of the rivers. 

A book of how to raise great weights by the simple increase of the 

A book of how to guard against the rush of rivers so that cities may 
not be struck by them. 

J B.M. 35 r. 

Of the inequality in the hollow of a ship. 

Book of the inequality of the curve of the sides of ships. 

Book of the inequality in the position of the helm. 

Book of the inequality in the keel of ships. 

Book of the difference in the holes through which water is poured out. 

Book of the water contained in vessels with air and of its movements. 

Book of the motion of water through a syphon. 

Book of the clashing together and concourse of water proceeding 
from different directions. 

Book of the varying shapes of the banks along which the rivers pass. 

Book of the various shoals formed below the locks of the rivers. 

Book of the twistings and bendings of the currents of the rivers. 

Book of the different places whence the waters of the rivers are 



Book of the shapes of the banks of the rivers and their permanence. 

Book of the perpendicular fall of water upon various objects. 

Book of the course of water when impeded in various positions. 

Book of the various shapes of the obstacles which impede the course 
of the waters. 

Book of the hollow or rotundity formed at the bottom round the 
various obstacles. 

Book of how to conduct navigable canals over or beneath the rivers 
which intersect them. 

Book of the soils which drink up the waters of the canals and of the 
means of protection. 

Book of the creation of channels for rivers which quit their bed when 
it is filled up with soil. 

^ B.M. 45 r. 

\Of water\ 

This wears away the lofty summits of the mountains. It lays bare 
and carries away the great rocks. It drives away the sea from its ancient 
shores for it raises its base with the soil that it carries there. It shatters 
and devastates the high banks; nor can any stability ever be discerned 
in these which its nature does not suddenly bring to naught. It seeks 
out with its rivers every sloping valley where it may carry off or deposit 
fresh soil. Wherefore many rivers may be said to be those through which 
all the element has passed, and the sea has gone back many times to the 
sea, and no part of the earth is so high but that the sea has been at its 
foundations, and no depth of the ocean is so low but that the loftiest 
mountains have their bases there. And so it is sometimes sharp and 
sometimes strong, sometimes acid and sometimes bitter, sometimes 
sweet and sometimes thick or thin, sometimes it is seen bringing hurt or 
pestilence, sometimes health-giving, sometimes poisonous. So one would 
say that it suffers change into as many natures as are the different 
places through which it passes. And as the mirror changes with the colour 
of its object so it changes with the nature of the place through which 
it passes: — health-giving, noisome, laxative, astringent, sulphurous, 
salt, incarnadined, mournful, raging, angry, red, yellow, green, black, 
blue, greasy, fat, thin. Sometimes it starts a conflagration, sometimes it 
extinguishes one; is warm and is cold; carries away or sets down, hollows 
out or raises up, tears down or establishes, fills up or empties, raises itself 
up or burrows down, speeds or is still, is the cause at times of life or 



death, of increase or privation, nourishes at times and at times does the 
contrary, at times has a tang of salt, at times is without savour, at times 
submerges the wide valleys with great floods. With time everything 

At times it goes twisting to the northern parts, eating away the base 
of its bank; at times it overthrows the bank opposite on the south; at times 
it turns towards the centre of the earth consuming the base which sup- 
ports it; at times leaps up seething and boiling towards the sky; at times 
revolving in a circle it confounds its course; at times it extends on the 
western side robbing the husbandmen of their tilth; at times it deposits 
the soil it has carried away in the eastern parts. And thus at times it 
digs out, and at times fills in where it has taken away and where it has 
made a deposit. Thus without any rest it is ever removing and consum- 
ing whatever borders upon it. So at times it is turbulent and goes raven- 
ing in fury, at times clear and tranquil it meanders playfully with gentle 
course among the fresh verdure. At times falls from the sky in rain or 
snow or hail; at times forms great clouds out of fine mist. At times moved 
of itself, at times by the force of others; at times gives increase to things 
that are born by its life-giving moisture, at times shows itself either fetid 
or full of pleasant odours. Without it nothing can exist among us. At 
times it is bathed in the hot element and dissolving into vapour becomes 
mingled with the atmosphere, and drawn upwards by the heat it rises 
until having found the cold region it is pressed closer together by its 
contrary nature, and the minute particles become attached together. 
And as when the hand under water squeezes a sponge which is well 
saturated so that the water shut up in it as it escapes through the crevices 
is driven into the rest and drives this from its position by its wave, so it 
is with the cold which the warm moisture compresses, for when it has 
reduced it to a more solid form the air that is pent up within it breaks by 
force the weakest part, and hisses just as though it was coming out of 
bellows when they are pressed down by an insupportable weight. And 
thus in various positions it drives away the lighter clouds which form 
obstacles in its course. 

B.M. 57 V. 

. . . stage of declivity. Water initiates its own movement. 

Book of the various ways of levelling waters. 

Book of how to divert rivers from places where they do damage. 



Book of how to straighten the course of rivers which cover too much 

Book of how to divide rivers into many branches and make them 

Book of how waters pass through seas with different movements. 

Book of how to deepen the beds of rivers by different currents of 

Book of how to control rivers so that the small beginnings of the 
damage they cause may not increase. 

Book of the different movements of waters which pass through 
channels of different forms. 

Book of how to prevent the small rivers diverting a larger one as their 
waters strike it. 

Book of how to ascertain the lowest level in the current of the surface 
of rivers. 

Book of the origin of rivers which flow from the lofty summits of the 

Book of the variety of the movements of waters in their rivers. 

B.M. 122 r, 

[Why the beds of straight rinsers are deeper in the centre than at the sides'] 

The current of a straight river is higher in the centre than at the 
sides, and rises towards the sky with greater waves and turns in greater 
depth towards the centre of the earth. 

And this occurs because the current is the clashing together or inter- 
section of the reflex movement of the waves, which leap back after 
striking against the bank and running back to the opposite bank clash 
with the contrary movements, and these resisting each other and neither 
being able to penetrate into the other leap back high out of the water, 
and then falling back —having acquired weight while in the air— plunge 
beneath the water there where they strike it. 

■> B.M. 135 V. 

How rivers widen their valleys and wear away the roots of the 
mountains at their sides: 

The bases of the hills as their valleys grow deeper are bent back 
towards the course of the river, as though they should wish to 
demand back from the speeding river the soil of which it has despoiled 

This proceeds from the nineteenth of this treatise which says: the 



current of the river eats away the base of the mountain on one side where 
it strikes and gives it back to the opposite side to which it is deflected. 

In great valleys the river changes its bed. 

The rivers in great valleys make greater changes in their beds in 
proportion as they are farther away from the roots of the mountains. 
This is proved by the ninth of this which says: the largest rivers flow 
through the largest valleys which have been made by them, and by 
reason of their size they are continually consuming the waves that flow 
from their banks, carrying them always back to the current of the river. 


The mouths of rivers are continually bending and descending behind 
the course of their principal stream, and this proceeds from the former 
[rule] which says: water takes away with its wave from the bank where it 
strikes and gives back to the opposite bank where it is deflected. 

Valleys are continually growing deeper. 

Valleys continually grow wider and deeper and rivers continually 
change their position. i6i r 


The water which falls in a perpendicular line through a round pipe 
upon a level place will make a circumambient wave round the site of its 
percussion, within the circumference of which the water will move very 
rapidly and be spread very thinly round about this place which has been 
struck, and at the end it will strike into the wave produced by it which 
seeks to return to the place of the percussion. , 

^ ^ B.M. 167 V. 

Water is that which serves the vital humour of this arid earth. 

It is the cause which moves it through its veins contrary to the 
natural course (desire) of weighty things; it is like chat which moves the 
humours in all kinds of living bodies, and ... 

And as the water is driven up from the lower part of the vine towards 
its severed stems and afterwards falls back to its roots, penetrates these 
and rises again anew, so from the lowest depth of the sea the water rises 
to the tops of the mountains, and falls down through their burst veins and 
returns to the sea and rises again anew. Thus up and down, in and out, 
unresting, now with fortuitous, and now with natural motionj now in its 



liberty and now constrained by its mover, it goes revolving and, after 
returning in force to its mover, rises again anew and then falls anew; so 
as one part rises the other descends. 

Thus from the lowest depths of the sea the water rises up to the 
summits of the mountains and falls down low through the burst veins, 
and at the same time other water is rising: so the whole element ranges 
about and makes its passage many times through the rivers that fall into 
the sea. 

At one time it becomes changed to the loftiest clouds, and afterwards 
it is pent up within the deep caverns of the earth. 

It has nothing of itself, but moves and takes everything, as is clearly 
shown when it is distilled. 

Thus hither and thither, up and down, it ranges, never resting at all 
in quietude, always flowing to help wherever the vital humour fails. 

Now taking away the soil, now adding to it, here depositing logs 
there stones here bearing sand there mud, with nothing stable in bed or 

Now rushing on with headlong course, now descending in tran- 
quillity, now showing itself with fierce aspect, now appearing bright and 
calm, now mingling with the air in fine spray, now falling down in tem- 
pestuous rain; now changed to snow or storms of hail, now bathing the 
air with fine rain; so also now turning to ice and now hot; never keeping 
any stability; now rising aloft in thin cloud, compressing the air where it 
shuts it in, so that it moves through the other air after the fashion of a 
sponge squeezed beneath the water, when what is enclosed within it is 
driven out through the rest of the water. b m 210 r 

The heat that is poured into animated bodies moves the humours 
which nourish them. 

The movement made by this humour is the conservation of itself and 
the vivification of the body which contains it. 

Water is that which serves the vital humour of the arid earth; it is 

poured within it, and flowing with unceasing vigour through the 
spreading veins it replenishes all the parts that depend of necessity on 
this humour. 

And it flows from the vast depths of the mighty ocean in the deep 
wide caverns that lie hid within the bowels of the earth, whence through 
the spreading veins upwards against its natural course in continual ascent 


to the high summits of the mountains it returns through the burst veins 
to the deep. 

Water is that which serves the vital humour of the arid earth; and 
the cause which moves it through the veins is just that which moves the 
humours in all the different species of animated bodies. ^ ^ ^ 

Water which serves as the vital humour of the arid earth and for this 
same cause moves through the spreading veins, is poured into it and works 
within it as does the blood in human bodies. 

The same cause moves the water through its spreading veins as that 
which moves the blood in the human species, and as through the burst 
veins in the top of a man the blood from below issues forth, so through 
the burst veins in the summits of the mountains the waters from below 
are poured out. 

Water after having issued forth from the veins of the earth is aban- 
doned by the moving cause which led it there. 

Water in falling from the high summits observes in its movement the 
desire of all the other heavy things. bm 234 V 

And that which with the utmost admiration of those who contem- 
plate it raises itself from the lowest depth of the sea to the highest sum- 
mits of the mountains, and pouring through the broken veins returns to 
the shallow parts of the sea, and again rises with swiftness and returns in 
like descent, and thus in course of time its whole element circulates. 

So from high to low, so passing in and out, now with natural and 
now with fortuitous movement it proceeds, together and united. So 
with continual revolution it goes ranging round, after the manner of the 
water of the vine, which as it pours through its severed branches and 
falls back upon its roots rises again through the passages, and falling 
back returns in a similar revolution. 

The water which sees the air through the broken veins of the high 
summits of the mountains, is suddenly abandoned by the power which 
led it there; and when the water escapes from the forces which raise it 
to a height it resumes in liberty its natural course. 

In the same way, so does the water that rises from the low roots of the 
vine to its lofty summit, and falling through the severed branches upon 
the primal roots mounts anew to the place whence it fell. 

^ B.M. 235 r. 



Water is just that which is appointed to serve as the vital humour of 
this arid earth, and the cause which moves it through its spreading veins, 
contrary to the natural course of heavy things, is just what moves the 
humours in all the species of animated bodies. 

This it is which to the complete stupefaction of the beholders rises 
from the lowest depths of the sea to the highest summits of the moun- 
tains, and pouring out through the burst veins returns to the depths of 
the sea and rises again swiftly and again descends as aforesaid. So from 
the outer parts, to the inner, so turning from the lower to the higher, at 
times it rises in fortuitous movement, at times rushes down in natural 
course. So combining these two movements in perpetual revolution it 
goes ranging through the channels of the earth. b m 236 v 


Either the water has weight or it has not weight. And if it has weight, 
why does not it bend the leaves borne on the bed where it rests? And if it 
does not bend them, it does not give its gravity to the bottom of the 
water. And if it does not give its gravity, what supports it? Its bed 
supports it, but it does not receive weight, because it is proved that water 
has no weight except above an element lighter than itself such as air and 
fire, and other liquids such as oil and the like. And if this is the case, why 
does a vase in the air weigh more when full of water than when full of 
air? The water does not weigh on their sides, but the vase when filled 
has weight in the air, which it would not have under water except to the 
extent of the weight of the material of which the vase is made. And the 
sea does the same upon its vase the earth, and the shores uncovered to 
the air are the lips of the vase that receives it. Which vase, being con- 
joined to the rest of the earth, throws its weight upon the air of its 
antipodes in the increase of the sea, because such antipodean seas balance 
each other in their weights through being opposite; and the inequality 
produced their weights, and from this caused the sea to be changing its 
position continually, the centre of gravity of the earth together with the 
water also changing its position. 


Because « c is of a width similar to a 0, and in like manner because 
m i is slightly less, these waters will be almost all at one level. 

Forster ni 32 v. 


The water a b will be very considerably higher than the water d e. 

The water r m will be almost equal, and the part o of the back-current 
will be extremely shallow and will hollow out the bed; / will be higher 
by reason of the percussion, x lower at the mill ... m 33 r 


When within the smooth water you see a spreading eddy there is a 
faU and rebound of water. ^ 


Why do the lines of the water pouring into a hole not direct them- 

selves to its centre? 

Forster in 75 V. 

Why do the circles of the water not break when they intersect? 

Forster ni 76 r. 

Why the water is higher in one part of the sea or river than in another, 
and why in many rapidly moving eddies the water is lower in the centre 
of the eddies than at the sides. 

On the Movements of Liquids by Galen. 

Quaderni ii 16 r. 

Water cannot move of itself unless it descends, and if it moves with- 
out descending it is moved by something else, and if it moves without 
being moved by anything else it is a reflex movement and of short life. 

Quaderni II 16 V. 

On how to bend the course of a river through its valley. 

And you who desire to control the course of the river and to be 
obeyed by it, you only need to cause its current to bend, for where this 
bends it wears away the bottom and draws after it all the rest of the water 

of its river. _ ' . 

Quaderm iv 2 r. 


The current of wateris the concourse of the reflections which rebound 
from the bank of the river towards its centre, in which concourse the 
two streams of water thrown back from the opposite banks of the river 
encounter each other; and these waters as they encounter each other 
produce the biggest waves of the river, and as these fall back into the 
water they penetrate it and strike against the bottom as though they 

Royal Library^ Windsor 


were a substance heavier than the rest of the water, and rub against 
the bottom, ploughing it up and consuming it, and carrying off and 
transporting with them the material they have dislodged. And therefore 
the greatest depth of the water of a river is always below the greatest 

It is possible for water in a brief time to perforate and make a passage 

through stone. 

Quaderni iv 3 r. 

Watch the movement of the surface of water, how like it is to that of 

hair, which has two movements, one following the undulation of the 

surface, the other the lines of the curves: thus water forms whirling 

eddies, part following the impetus of the chief current, part the rising and 

falling movement. „„ , 

° Windsor. Drawings 12579 r. 

The movement of the wave is swifter than the movement of the 
water that produces it. This is seen by throwing a stone into still water, 
for it creates around the spot where it strikes a circular movement which 
is swift, and the water which creates this circular swelling does not move 
from its position nor do the objects which float on the surface of the 

Leic. 14 V. 

\With drawing of section of rinser in which are the words ^Arno\ ‘ Rif redi\ 

When a lesser river pours its waters into a greater and this greater 
flows from the opposite bank, the course of the lesser river will be bent 
by the onset of the greater. And this occurs because when this greater 
river fills up the whole of its bed with water it comes to form an eddy 
under the mouth of this river, and thus drives with it the water that has 
been poured out by the lesser river. When the lesser river pours its 
waters into the greater river which has its current crossing the mouth of 
the lesser river, its waters will bend in the direction of the current of the 
greater river. . . 

o Leic. I c r. 


Book I of water in itself 
Book 2 of the sea 
Book 3 of the springs 

Book 4 of rivers 

Book 5 of the nature of the depths 

Book 6 of the objects 

Book 7 of different kinds of gravel 

Book 8 of the surface of water 

Book 9 of the things that move in it 

Book I o of the means of repairing [the banks of] rivers 

Book 1 1 of conduits 

Book 1 2 of canals 

Book 1 3 of machines turned by water 
Book 14 of how to make water ascend 

Book 1 5 of the things which are consumed by water. ^ 

Whether the flow and ebb are caused by the moon or sun, or are the 
breathing of this machine of the earth. How the flow and ebb differ in 
different countries and seas. 

How in the end the mountains will be levelled by the waters, seeing 
that they wash away the earth which covers them and uncover their rocks, 
which begin to crumble and are being continually changed into soil 
subdued alike by heat and frost. The waters wear away their bases and 
the mountains bit by bit fall in ruin into the rivers which have worn 
away their bases, and by reason of this ruin the waters rise in a swirling 
flood and form great seas. 

How in violent tempests the waves throw down every light thing 
and suck much earth into the sea, which causes the water of the sea to be 
turbid over a wide space. 

How loose stones at the base of wide steep-sided valleys when they 
have been struck by the waves become rounded bodies, and many things 
do the same when pushed or sucked into the sea by these waves. 

How the waves quiet down and make long stretches of calm water 
within the sea without any movement when two opposite winds meet 
together at this spot; thus at these meeting places various shapes made up 
of calm sea are visible surrounded by the tiny waves of a moderate sea. 



Water of itself does not move unless it descends. 

That water will be highest which is farthest removed from the centre 
of its sphere. And that surface of water is said to be lowest which is 
nearest to the centre of its sphere. 

No surface of water which is contiguous to the air is lower than the 
surface of its sphere. The waters of the salt seas are fresh at their maxi- 
mum depth. The waters range with perpetual movement from the 
lowest depths of the seas to the topmost summits of the mountains, not 
following the law of heavy things; and in this instance its action resembles 
that of the blood of animals which is always moving from the sea of the 
heart and flowing towards the summit of their head; and so when a vein 
there has burst open, as one sees if a vein bursts in the nose, the whole 
of the blood from below rises up to the height where the vein has burst. 

When the water gushes forth from the burst vein in the earth it 
follows the law of other things which are heavier than the air and so 
always seeks the low places. 

That water will be swifter which descends by the less slanting line. 
And that water will be slower which moves along a more slanting line. 
The Nile and the other rivers of great size have very many times poured 
out the whole of the element of water and restored it to the sea. The 
veins flow with infinite ramifications through the body of the earth. 
The waters assume as many different natures as the places are different 
through which they pass. If it were possible to make a well which should 
pass through the earth on the opposite side and for a river to descend 
through this well, the head of the river which entered there first would 
descend through this well and pass the centre of the elements without 
making any reflex movement, and it would pour as much water on the 
far side of this centre as it had from the opposite side. 

And if, because of some deep valley, the line on the opposite side of 
the well were shorter than on this side, this water would fill up the valley, 
however large it was, until it equalled the weight of the water in the well, 
although in some part the centre (of gravity) of the water and of the 
earth united together would move somewhat from its first position 
through the weight of the water, which would be increased on the 
opposite side of the earth where it was not at first. The centre (of 
gravity) of the water and earth joined together is moved when the 
weight of the sea moves because it is carried by the winds. Leic. 21 v. 


T H I R T Y - N I N E C A S E S 

How the bottoms of rivers and ditches become trampled by big 
animals and this causes the muddy waters to escape and they thus leave 
in their course the soil in which they were loitering. How in the manner 
described above canals may be constructed through level lands. How to 
convey away the soil from canals which have become choked up with 
mud by the opening of certain sluices which are moved upwards by the 

How one ought to straighten rivers. How one ought so to provide 
that rivers do not sweep away other men’s possessions. How one ought 
to maintain the beds of rivers. How one ought to maintain the banks. 
How the banks when broken should be repaired. How one ought to 
regulate the impetus of rivers in order to strike terror into the enemy 
so that he may not enter the valleys of this river to damage them. 

How the river in order to be crossed by your army ought to be con- 
verted into many small branches. How one ought to ford rivers below 
the rows of horses so that they may protect the infantry from the rush 
of the water. 

How by the use of wine-skins an army is able to cross a river by 
swimming. How the shores of all the seas that touch one another are of 
equal height, and are the lowest part of the land which meets the air. 
Of the manner of swimming of fishes; of the way in which they leap out 
of the water as may be seen with dolphins, for it seems a marvellous thing 
to make a leap upon something which does not stand firm but slips away. 

Of the manner of swimming of animals of long shape such as eels and 
the like. Of the way of swimming against the currents and great falls of 
rivers. Of the way in which fishes swim when they are round in shape. 
How animals which do not have the hoof cleft asunder are not able to 
swim. How all the other animals which have feet with toes are by nature 
able to swim, except man. In what way a man ought to learn to swim. 
Of the way in which a man should rest upon the water. How a man 
ought to defend himself against the whirlpools or eddies of the waters 
which suck him down to the bottom. How a man when sucked down to 
the bottom has to seek the reflex current which will cast him out of the 
depths. How he ought to propel himself with his arms. How he ought 
to swim on his back. 

How he can only remain under water for such time as he can hold 
his breath. 


How by an appliance many are able to remain for some time under 
water. How and why I do not describe my method of remaining under 
water for as long a time as I can remain without food; and this I do not 
publish or divulge on account of the evil nature of men who would 
practice assassinations at the bottom of the seas by breaking the ships in 
their lowest parts and sinking them together with the crews who are in 
them ; and although I will furnish particulars of others they are such as 
are not dangerous, for above the surface of the water emerges the mouth 
of the tube by which they draw in breath, supported upon wine-skins 
or pieces of cork. 

How the waves of the seas continually consume their promontories 
and rocks. How the shores of the seas grow continually towards the 
centre of the sea. The reason why the gulfs of the seas are created. The 
cause why the gulfs become filled up with earth or seaweed. 

The cause why round about the shores of the seas there is found a 
large high bank called the mound of the sea. 

Why the waves are higher when they touch the bottom nearer to the 
shore than they are on the high sea. 

How at the mouths of certain valleys the gusts of wind strike down 
upon the waters and scoop them out in a great hollow, and carry the 
water up into the air in the shape of a column and of the colour of 

And this same thing I once saw taking place on a sand-bank in the 
Arno, where the sand was hollowed out to a depth of more than a man’s 
stature, and the gravel of it was removed and whirled a great distance 
apart, and assumed in the air the form of a mighty campanile; and the 
summit of it grew like the branches of a great pine, and then it bent on 
meeting the swift wind which passed over the mountains. 

How the wave is least towards the approaching wind because the 
bank serves it as a shield. 

How the water that finds itself between the percussions of the waves 
of the sea becomes changed into mist. 

Of eddies wide at the mouth and narrow at the base. 

Of eddies very wide at the base and narrow above. 

Of eddies of the shape of a column. 

Of eddies formed between two masses of water that rub together. 

Leic, 22 V. 

How waves do not penetrate one another but leap back from the 


place where they have struck; and every reflex movement flies away at 
equal angles from the striking place. 

The reflex movement of water within water will always be of the 
same shape as its falling movement. By this reflex movement I do not 
mean that which springs back within the air but that which follows along 
its surface. » 

As the wave of the sand moves considerably more slowly than the 
wave of the water that produces it, so the wave of the water created by 
the wind is much slower than the wave of the wind that produces it, that 
is the wave of the air. The wave of the air performs the same function 
within the element of fire as does the wave of the water within the air, or 
the wave of the sand, that is earth, within the water; and their movements 
are in the same proportion one to another as is that of the motive powers 
within them. 

The more powerful current will cleave asunder the less powerful and 
pass through the middle of it. Currents of equal power which clash to- 
gether leap back from the site of their percussion. A whole mass of 
water in its breadth, depth and height is full of innumerable varieties 
of movements, as is shown on the surface of water of a moderate degree of 
turbulence, in which one sees continually gurglings and vortices, with 
various eddies formed of the more turbid water from the bottom that 
rises to the surface. How every seven years the waters of the Adige rise 
and then fall, and it makes a famine as it rises. ^ . 

Leic. 23 r. 

How water has tenacity in itself and cohesion between its particles. 
This is seen from the fact that a drop before separating itself from the 
remainder stretches itself out as far as it can, and offers resistance in its 
union until it is conquered by the excessive weight of the water which 
is continually increasing upon it. How water serves as a magnet for 
other water. This is seen in the process of a drop becoming detached 
from the remainder, this remainder being stretched out as far as it can 
through the weight of the drop which is extending it; and after the drop 
has been severed from this mass the mass returns upwards with a move- 
ment contrary to the nature of heavy things. It may be seen how the 
larger drop of water instantly takes up into itself the smaller drops which 
come into contact with it; and the minute particles of moisture diffused 


through the air act in the same way, for they become compressed, making 
themselves a magnet one for another until at last their weight so increases 
as to conquer the resistance of the air that first sustained them, and so 
they descend in the form of rain. 

It may be shown with a bubble of water how this water is of such 
uniform fineness that it clothes an almost spherical body formed out of 
air somewhat thicker than the other; and reason shows us this because 
as it breaks it makes a certain amount of noise. ^ . 

Leic. 23 V. 

It is possible to devise obstructions which will preserve the embank- 
ment against the friction of the current. 

You should therefore cause blocks of coarse shingle to be constructed 
ten braccia apart; and let them be ten braccia wide with height varying 
according to the height of the embankment and of a thickness of three 
braccia. And they should be set to slant in the direction from which the 
water comes; and each of itself will serve as a shield to the water and 
throw it back towards the centre of the stream. 

When the obstruction covered by the water slants very considerably 
in the direction from which the water comes, the stroke of the water will 
only cause a small hollow in front of this obstruction and it will deposit 
a considerable quantity of soil behind it. 

If the obstruction is entirely upright and the water flows over it it will 
form a deep hollow in front of it and will only deposit a small amount of 
soil behind it. And if the obstruction has a lesser obstruction in front of 
it which leans against it there will be no hollow in front of this lesser 
obstruction for so far as its bulk extends. If the obstruction have another 
near behind it the hill of sand will be suddenly cut and dug out in a new 

How the rivers, in their great floods, fill up all their greatest depths 
with sand or stones, except the places where the river is confined, as 
when it passes through the arches of bridges or other constricted places; 
and it does this because behind these arches it strikes against the front 
of their columns, and rises in a swirling flood, and raises itself, and so 
with fury makes up for the delay that has taken place before the said 
bridge or other object. ^ 

If the obstructions of the waters are permanent the deep places of 
the rivers caused by them will also be permanent. And if the obstructjoa 


of these waters is movable the deep places caused by it will also be mov- 
able. And if the movable obstruction is near the bank of the river it 
immediately will become the cause of bending the whole river; and this 
is due to the fact that the water which passes between the obstruction 
and the bank hollows out this bank. And even though the obstruction 
proceed upon the bed of the river behind the current of the waters, it 
does not follow that the concavity already made in the bank will not 
proceed continually to grow and increase because of the water that ranges 
within it, as is shown by the fourth of the third; and that the water which 
leaps back from it to the opposite bank will not create another similar 
concavity in this bank; and this will then proceed continuously to in- 
crease, and then it returns leaping back beneath the first concavity; and 
so it proceeds time after time until this impetus is consumed amid the 
universal current of the river. 24 v 


These are the cases that have to stand in the beginning: 

The air which is submerged together with the water which has struck 
upon the other water returns to the air, penetrating the water in sinuous 
movement, changing its substance into a great number of forms. And 
this occurs because the light thing cannot remain under the heavy, 
rather is it continually pressed by the part of the liquid which rests upon 
it; and because the water that stands there perpendicular is more power- 
ful than the other in its descent, this water is always driven away by the 
part of the water that forms its coverings, and so moves continually side- 
ways where it is less heavy and in consequence offers less resistance, 
according to the fifth of the second. And because this has to make its 
movement by the shortest way it never spreads itself out from its path 
except to the extent to which it avoids that water which covers it above. 

When the air enclosed within the water has arrived at its surface it 
immediately forms the figure of a half-sphere, and this is clothed with 
an extremely thin film of water. This occurs of necessity because water 
has always cohesion in itself, and this is the more potent as the water is 
more sticky; and this air having reached the opening of the surface 
of the water and not finding there any further weight to press upon 
it, raises its head through the surface of the water with as great a 
weight of water joined to it as the aforesaid tenacity can have; and 
it stops there in a perfect circle as the base of a half sphere, which 

in , 


has the aforesaid perfection because its surface has been uniformly ex- 
panded by the uniform power of the air. And it cannot be more than 
a half-sphere because spherical bodies attain their greatest width at their 
diameter; and if this air that is enclosed were more than a half-sphere 
the base would be less than where the diametral line is, and consequently 
the arc of this half-sphere would not have shoulders or real resistance in 
its weakest, that is its widest part, and therefore it would come about that 
it would break in this spot of its greatest width, because the weakest part 
of any arc is always the end of its greatest width. 

The air emerges with impetus in spherical form clothed with an 
extremely thin film of water, away from the body of the water; and this air 
by reason of the weight that it has acquired cannot pour itself into the 
other air, but held back by the adhesiveness of the water with which this 
film was formed falls down again by its excess of weight, continually 
growing in circumference, because the amount of the air which at first 
was in the whole of the aforesaid spherical body is afterwards reduced 
by half, and this is of itself capable of containing all this air, so that this 
spherical body goes on descending so far towards the surface of the water 
that it unites with it, finding there as I have said before greater width 
than in its own diametral line. 

Nor has the air clothed with a thin film of water perfect sphericity 
in the aforesaid instance, because the part of the water with which this 
air is clothed, is heavier where it is more perpendicular to the centre of 
the circle, which makes itself the base of this half-sphere, and therefore 
in this position it lowers itself more; because that part of a thing sup- 
ported in its extremities is so much weaker as it is more distant from its 
foundation, and that thing descends more rapidly which has the weaker 
support. That part of the air clothed by a film of water will be of most 
perfect sphericity which is least in size; this is proved by the reason stated 
above, because these bodies are clothed with films of equal thickness: for 
if the air that escaped from the surface of the water was small in amount 
it raised up a small quantity of this film, and clothed itself in it; and since 
its lesser^ altitude is nearer its foundation than was that of a greater, it 
maintains itself more than this greater. The air which is subdued by the 
weight of the film of water which clothes it penetrates in minute particles 
through this film, and these, for the reason stated, cannot be separated 
from their state of connection or adhesion to it, and therefore through 
^ MS. has maggiore. 


the weight it has thus acquired it descends from the sides of this body, 
and remains joined to the base of the middle sphere of air from whence 
it descended. 

It breaks the middle sphere of the air clothed by the water in the 
third part of its curve; this is proved with the arches of walls, and there- 
fore I will not treat of it in these notes, but I will place it in the book 
where it is necessary. 

That part of the water is higher which is more remote from the centre 
of the sphere of fire and of the air and of the water, but not of the earth, 
because this has not a mathematical spherical shape; and for this reason 
the centre of its gravity is not concentric with the centre of the spheres 
of the other three elements. 

The water of itself does not move unless it descends: therefore, when 
it is in its sphere it does not have one part of itself lower than another, 
and therefore of itself it will not move unless it is moved by others: and 
the two aforesaid proofs are sufficient to prove that water is spherical and 
of itself without movement; and as a consequence all the waters that 
move of themselves are lower at one extremity than at the other, that is 
in their surface ; so finding the descent it runs there because there is no 
support for it there. 

How the air can never of itself remain beneath the water but always 
wishes to be above in its contact: in proof of this let it be supposed that 
there are three elements and that the earth is nothing and that one allows 
a quantity of water to fall through the air; this cannot stay above the 
air, because the weaker liquid body cannot support the heavier, and 
consequently the air since it is a body thinner than the water and there- 
fore is not able to support it will give it place; and this it will continue to 
do until the water has reached its lowest depth, that is assuming that it has 
not become evaporated or changed into air through its long friction with 
the air; but let us suppose that so much turns that a part arrives there: 
I say that after consuming its impetus between the reflex and falling 
movements which it would make around its centre it would come to a 
stop at this centre under all the sphere of air equally, because the centre 
of the elements is the lowest part that can be found in them, since the 
lowest is that part which is farthest removed from the greatest height of 
its whole. This is the conception. 

Water attracts other water to itself when it touches it: this is proved 
from the bubble formed by a reed with water and soap, because the 


hole, through which the air enters there into the body and enlarges it, 
immediately closes when the bubble is separated from the reed, running 
one of the sides of its lip against its opposite side, and joins itself with it 
and makes it firm. 

Also a small drop enters into the body of the other water. If you 
should grant me by the proof of these bubbles of water that water has 
tenacity though it be small and thin, you grant me that that which 
makes the part will make its whole. 

The bubble formed within the air by a reed, through which it is 
blown, does not fall in spherical shape, when it becomes detached because 
its excess of water runs below and makes it heavier there than else- 
where, and consequently the movement there is hurried, and breaks it 

above at a third. ' . 

Leic. 25 r. 

Every current has three central lines, which are situated in the middle 
of its greatest power: of these one is at the contact made by the water 
with the bed that receives it; the second is at the middle of its depth and 
width; the third is formed on the surface; but that of the middle is the 
principal one for it guides the whole course and divides all the reflex 
movements and turns them to their appointed directions. The higher 
central line of the current of the water is the upper line of the falling 
movement, and the lower of the reflex whirling movement, that is that 
which turns itself over and falls down upon the falling movement upon 
which it takes its leap; but let us leave the revolutions of the waters and 
their changes from below upwards as far as concerns these definitions, 
and speak only of the water remaining on the surface, that is as far as 
concerns its central lines. The central line of the surface of the current 
is always in the most prominent part of the water which surrounds the 
object struck by it; and the central line is only that which after striking 
upon a smooth-faced object falls back upon itself. The central line of the 
bottom of the current after striking upon the smooth object, is turned 
over towards the centre of the earth, and rambles about so much in 
scraping the bed that it makes a hollow large enough to contain its 
revolutions; and all the other lateral lines slope to the bed and hollow it. 
[To consider] whether the wave of the water causes the formation of the 
wave of sand above its bed or whether the wave of the bed is the cause 
of the wave on the surface of the water. [To consider the] difference 
between the waves, from knowing their depth: which may always be 

: ■■ 


discovered between the falling and the reflex movement of the waters. 
[To consider] how the least depth within the banks of any expanse of 
water will be found at the end of its reflex movement. How also the least 
depths of rivers will be found at the sides of the currents where they 
unite with other currents. [To consider] how in between two currents 
there are always shallows. The highest part of the surface of the water 
that strikes the object will strike it in its centre if it be of smooth front 
or pointed with sides of equal slant and length. But unless the angle is 
in the middle of the front of the object the highest elevation of the 
wave that strikes it will no longer be in the centre of this front but 
opposite to the aforesaid angle. The water of the surface that is moved 
in tiny ripples by the wind, always moves so much more swiftly than 
the wave of the water, in proportion as the wave is swifter than the 
natural movement of the water, and as the natural movement of the water 
is swifter than the wave of the sand, and as the wave of the sand is swifter 
than the wave of the earth that forms the river bank. But I ought first to 
say that the movement of the free air is so much swifter than the move- 
ment of the air that strikes the water, because that part of the wind that 
strikes the water is checked by the resistance of the surface of the water. 
All the waves of the sand which travel with the water are as much 
slower than the waves of the sand that travel with the wind as the move- 
ment of the water is slower than the movement of the wind. 

Leic. 25 V. 

In these eight sheets there are seven hundred and thirty conclusions 
as to water. 

When the wave has been driven on to the shore by the force of the 
wind it forms a mound by putting its upper part at the bottom, and 
turns back on this until it reaches the spot where it is beaten back anew 
by the succeeding wave which comes below it and turns it over on its 
back, and so overthrows the mound and beats it back again on the shore 
mentioned before; and so continues time after time; turning now to the 
shore with its upper movement and now with its lower fleeing away 
from it. 

How it is not possible to describe the process of the movement of 
water unless one first defines what gravity is and hpw it is created or 


As the wave after striking on the sea shore turns back along the bed 
of the sea behind its mound, it encounters the following wave which 
comes from the high sea, and breaks itself upon it and divides itself; 
part leaping towards the sky and then falling down and turning back, 
part towards the bed of the sea; and this continues towards the sea, carry- 
ing with it the lower part of the water that struck upon it. Were it not 
for it doing thus the seaweed and the wrack of the tempests would not 
be able to be carried from one shdre and deposited upon another. If 
the water of the sea turns towards the sea above its bed after the per- 
cussion made upon its shore, how can it carry with it the shells, molluscs, 
‘buovoli’, snails and other similar things produced in the bed of the sea, 
and throw them upon this shore? This movement of the aforesaid things 
towards the shore commences when the percussion of the falling wave 
divides the reflex wave into the aforesaid two parts, for the things raised 
from the bottom often leap up in the wave that returns to the shore, and 
being solid bodies are driven towards the mound, which then draws them 
back with it towards the sea; and so continues in succession until the 
storm begins to abate, and stage by stage it leaves them where the greater 
wave reaches, that is that as the succeeding wave does not return to the 
same mark where it had deposited the booty that it carried, this booty 
remains where it has been lefc by the wave; and this process continues as 
the waves grow less. There remain the things cast up by the sea within 
the space that lies between the first mound of the wave upon the 
shore and the mound made by the wave that oomes from the deep sea. 
If the whole sea rests and supports itself upon its bed the part of the sea 
rests upon the part of the bed: and as water possesses gravity when out 
of its element it ought to weigh down and press upon the things that 
rest on its bed. But we see the contrary, for there the seaweed and grass 
that grows in these depths are not bent or crushed upon the bottom but 
cleave it directly as though they were growing within the air. 

So we arrive at the conclusion that all the elements, though they are 
without weight in their own sphere, possess weight away from their 
sphere, that is away towards the sky, but not away towards the centre 
of the earth; because if it proceeds away towards this centre it finds 
an element heavier than itself, with its thinnest and lightest part 
touching an element lighter than itself, and the heavier part of the 
element is so placed as to be near the element that is heavier than 


How water when transformed becomes changed into wind which is 
so much drier as the process of transformation is more complete. 

How wind is generated by the coagulation of the water within the 
air, for the air hastens to where there is a lack of it, and so it flees from 
where it is in excess. How the air has a greater volume where there is 
more wind, because the air there is thicker. 

How the winds are strongest in the moist seasons, and more so in 
the rains than in clear weather. How great winds proceed from the 
mountains that are covered with snow; and to this the sailors bear witness 
for they experience it every day. And this is brought about through the 
fact of the snow becoming dissolved in the air, and being dissolved in 
very fine particles; hence philosophers say that there are dry land 
vapours; as to which I have nothing to say. 

How the wind, proceeding from the cloud, is not exhaled in a circle 
through every line away from the cloud, because it acquires more weight 
than the air through which it passes, and so of necessity is bent to the 
ground as are all the things that are heavier than the air, and it rambles 
through it, driven by that which follows, which is created behind it, or 
by the impetus it has acquired from its past movement. ^ 

That water may have tenacity and cohesion together is quite clearly 
shown in small quantities of water, where the drop, in the process of 
separating itself from the rest, before it falls becomes as elongated as 
possible, until the weight of the drop renders the tenacity by which it is 
suspended so thin that this tenacity, overcome by the excessive weight, 
suddenly yields and breaks and becomes separated from the aforesaid 
drop, and returns upwards contrary to the natural course of its gravity, 
nor does it move from there any more until it is again driven down by 
the weight which has been reformed. From this proposition two 
conclusions follow, of which the first is that the drop has cohesion 
and nerve-structure in common with the water with which it is 
joined; secondly that the water drawn by force breaks its cohesion, 
and the part that extends to the break is drawn up by the remainder in 
the same manner as is the iron by the magnet. The same is seen with 
water passing through a filter, for the greater weight of the water that 
is outside the vessel draws back the lesser weight of the water which this 
filter holds back curved within the vessel. 

One may offer a proof of the tenacity of water and set it out in 

■ ii8 ■ 


proportion, thus: — if a drop of water of two grains is supported by 
water of the volume of half a drop by how much will a pound be sup- 
ported? And in this way we shall arrive near the truth. The sand weighs 
more than the water; and if there be left within the air in continuous line 
a quantity of sand and a quantity of water, separated from the sand 
but of the same weight as the sand, without doubt the movement of 
the sand will be slower than that of the water; and this comes about be- 
cause the lower part of the water draws down the water that is joined to 
it above, and consequently it makes itself all one body and weighs all 
together upon the air, which opens below to give it place. This does not 
happen however with the sand, for in itself it is all separated and loose, 
and the whole of the amount falls with the same speed that one of its 
grains would, as they are all equal. So that we may conclude that the 
continuous descent of the water as it falls through the air proceeds with 
the speed that its weight requires, because it is a united and con- 
tinuous quantity; and the sand of the same weight which descends from 
the same position of the water only proceeds with as much speed as is 
required by the weight of one of its medium-sized grains, for those that 
are larger descend more swiftly than those of medium size, and the less 
descend more slowly. 

For if water has in itself adhesiveness and a tendency to unite, the 
water that is poured from a siphon, being surrounded by air, does not 
draw itself after that of the siphon; and experience shows us that unless 
the outlet of the water of the siphon is lower than its entrance into the 
pipe, the water that continues below its outlet from the pipe will never 
draw itself after that of the vessel. If in the descent of the water 
within the air the water above, which drives it downwards, does not 
descend there with the same speed of a greater, that below will divide 
itself from that above, if it is swifter. 

How the water that descends through the air breaks because the 
air through which it passes divides it. How the water which is divided 
as it descends continuously through the air has a medium of spray, 
which extends from one divided part to the other, and binds them up 
together. How all the volume of the water which descends through 
the air in continuous quantities, is constrained to descend with equal 
movement, because where it made itself swifter it would separate itself 
from the part that was slower, and where it made itself slower it would 
be doubled and multiplied by the part that was swifter. How as great 



a weight of water is displaced as the weight of the thing that is supported 
by this water. How in the same slant, the water will make itself so 
much slower in its movement as it is lower upon its bed. How water 
made to gyrate in swift movement in a vessel by the hands of him 
who is whirling it round becomes extremely concave at the centre. 

Of the great difference there is when water is whirled in a vessel, 
according to whether the hand is held near to the centre of this vessel 
or near the larger circle of the surface of the water. How the hand 
drawn frequently across the vessel up and down produces strange move- 
ments and surfaces of different heights. What water does when made to 
gyrate in an oval vessel. What water does when made to gyrate in a 
vessel with corners. What water does in a vessel that is struck from 
below. What water does in a vessel that is struck at the side. What water 
does in a vessel when the spot is struck on which it is standing. 

Of the music of water falling into its vessel. ^ 

How nothing evaporates except by means of moisture, which after 
having been evaporated preserves in itself the nature of the body in 
which it was infused. How the rumbling produced by the earthquake 
in the body of the earth proceeds from the destruction of places, torn 
open by force by the winds which continually strike upon the beds of 
their great caverns or lakes, covered and shut in within the earth. 

But the tempest of the sea, snatched from its shores and borne far 
over the sea will be turned back, and especially if there is great depth 
there; and this happens because during a storm the wave of the sea does 
not penetrate to its great depths; and if it should chance to reach there 
it changes its movement. The water of the sea during a storm makes a 
great movement on its bed in a different direction from that of its surface. 

The dams of rivers if not of too great width may be made in this 
manner: a stake such as pile-drivers use should be fixed every three 
braccia, as big as possible and the bigger the better; and their tops should 
be of uniform height. On these a log of the shape of a beam should be 
fastened very firmly; next long trunks with all their branches should be 
taken and laid upon the aforesaid beam, and they should be fastened to 
it by using one of the branches as a hook; and this process should be 
repeated as often as possible, placing the branches towards the coming of 
the water; and they shotild then be loaded with shingle and stones; and 
after the first flood it is left grounded. But remember to fix the branches 



so that they are raised up and make them fall with the others. And if 
the river should be narrow you set the beam across from one bank to 
the other and fix it well; and set the aforesaid branches to lean upon it 
fastened with their natural hooks. The beam here is only for the purpose 
of holding the heads of the logs so that they do not drop down; and the 
branches which stand against the course of the river laden with stones, are 
not allowed to push this beam or bend its direction because it is held by 
their natural hooks, and their buried branches do not allow them to 
move or to tear away the said hooks. 

How the diverting of rivers ought to be carried on when the water 
has completely lost the fury of its current, that is when it shows itself 
tired. How with a small dam a river may be diverted by aiding and 
increasing the line where it shows that it wishes to turn of itself. 

How a river may be diverted by a few stones if one understands the 
line of its current; and this movement may be made in the aforesaid line 
of the water. How the dams of the rivers should never be formed by 
placing stakes in deep places but in the more shallow places. How the 
dams of the rivers when formed of masonry ought to be constructed in 
the deepest parts of the rivers, so that they may be less in the power of 
the water which undermines them. How the dams of the rivers ought to 
to be made in the fields away from the rivers and then the said river be 
directed against them. How the bridges ought also to be made in the 
fields in that part where it is afterwards intended to direct the river. 

Leic. 27 V. 

The ramifications of the springs of water are all joined together in 
this earth, as are those of the blood in other animals; and they are in 
continual revolution, and thus vivified they are perpetually wearing away 
the places in which they move, both those within the earth and those on 
the surface of it; and the rivers universally pour out much more water 
now than formerly: for which reason the surface of the sea is somewhat 
lowered towards the centre of the world as it has had to fill up the 
vacuum caused by this increase in these springs; of which I shall speak 
presently. The heat of the fire generated within the body of the earth 
warms the waters which are pent up within it in the great caverns and 
other hollow places; and this heat causes these waters to boil and pass 
into vapour and raise themselves up to the roofs of the said caverns, and 
penetrate through the crevices in the mountains up to their greatest 
height, where coming upon the cold it is suddenly changed into water, 



as one sees happen in a retort, and goes falling down again and forming 
the beginnings of rivers which are afterwards seen descending from 
them. But when the great frosts drive back the heat towards the centre 
of the world, this heat becomes more powerful and causes a greater 
vaporisation of the aforesaid water; and this vapour heating the caverns 
round which it moves in circles cannot form itself into water as it usually 
does: as is seen in the making of aqua vitse, for unless the vapour of the 
wine passed through fresh water it would not change into aqua vitse, but 
would go back and become at last so much condensed as to break down 
every obstacle. We may say the same of water heated in the bowels of 
the earth, which not finding in its passage places of such freshness as 
harmonises with it, does not form itself into water as formerly, but con- 
denses and hardens like fire multiplied and condensed within a mortar, 
which becomes harder and more powerful than the substance that con- 
tains it, and so unless it be suddenly dissolved in smoke it instantly 
hurls itself forward, breaking and destroying whatever opposes its 
growth. It is the same with the aforesaid steam from the water, for it 
bursts forth within the bowels of the earth in divers places; ranging about 
and roaring with great tumult until it reaches the surface; and with a 
mighty earthquake makes whole regions tremble, and often makes 
mountains fall in ruin, and lays waste cities and lands in divers parts, and 
with a mighty hurricane bursts its way forth through the cracks in the 
earth which it has made; and so by thus escaping it consumes its own 
might. The wind is formed by the water in the air through the processes 
of the dissolving and the formation of clouds; that is that when the cloud 
is dissolved it becomes changed into air and increases in its bulk fitfully 
and irregularly, since the process of its dissolution does not work uni- 
formly; because the cloud is in itself of varying thinness and density, 
consequently the part that is thinnest is dissolved most rapidly, and the 
thick part offers most resistance to this process: this therefore is the cause 
why the movement of this wind does not proceed uniformly. 

And when the cloud is created it also generates wind, since every 
movement is created from excess or scarcity; therefore in the creation 
of the cloud it attracts to itself the surrounding air, and so becomes con- 
densed, because the damp air was drawn from the warm into the cold 
region which lies above the clouds; consequently as it has to make water 
from air which was at first swollen by it, it is necessary for a great quan- 
tity of air to rush together in order to create the cloud; and since it can- 



not make a vacuum, the air rushes in to fill up with itself the space that 
has been left by the [former] air, which was first condensed and then 
transformed into a dense cloud. In this circumstance the wind rushes 
through the air, and does not touch the earth, except on the summits of 
the high mountains; it cannot draw the air from the earth, because there 
would then be a vacuum between the earth and the cloud; and it draws 
but little air through the traverse and draws it more abundantly 
through every line. I have already had an opportunity of observing 
this process; and on one occasion above Milan, over in the direction of 
Lake Maggiore, I saw a cloud shaped like a huge mountain, made up 
of banks of fire, because the rays of the sun which was then setting red 
on the horizon had dyed it with their colour. 

This great cloud drew to itself all the little clouds which were round 
about it. And the great cloud remained stationary, and it retained the 
light of the sun on its apex for an hour and a half after, sunset, so enormous 
was its size. And about two hours after night had fallen there arose a 
stupendous storm of wind. 

And this, as it became closed up, caused the air which was pent up 
within it, being compressed by the condensation of the cloud, to burst 
through and escape by the weakest part, rushing through the air with 
incessant tumult, acting in the same way as a sponge when squeezed by 
the hand underneath the water, for the water with which it is soaked 
escapes between the fingers of the hand that squeezes it, and rushes 
swiftly through the other water. So it is with the cloud, driven back and 
compressed by the cold that clothes it round, driving away the air with 
its own impetus, and striking it through the other air, until the heat that 
is mingled with the moisture of the cloud that has drawn it to so great a 
height flies back towards the centre of the cloud, escaping the cold which 
is its contrary, and having approached towards the centre becomes 
powerful, and consequently takes fire and makes a sudden emission of 
damp steam, which surrounds it and creates a furious wind that moves 
with the fire thrown out by the increasing pressure of the steam; and 
thus fire is expelled from the cloud as is the flame from the mortar, by 
the wind increasing behind it; and so this flame compressed by the cloud 
issues forth, and spreads through the air, with the more radiance in pro- 
portion as the fire of which it is formed is more concentrated and of 
greater heat: and this is the thunderbolt which afterwards ruins and 
smashes in pieces whatever opposes its destined course. 

, '123 


I have already seen fire created under the water with the movement 
of a wheel which whirled its arms; and it will do the same at any depth 
however great. 

If the river be turned at the upheaval of the earthquake, it 
will no longer run forwards but will return into the body of the earth, as 
does the river Euphrates; and let this serve for any of those at Bologna 
who lament over their rivers. Leic. 28 r. 

That water will rise higher with its wave than the common surface of 
the water of the lake, when it is nearer the spot at which it falls into the 
lake. When the waters from different parts meet together in a hole that 
is in the bed of the river this water will be bored through as far as the 
entrance of the hole, and the cavity so made will be filled with air as far 
as the bed of the water. 

The revolving movement cannot be continued strictly below the 
water unless this revolving mass of water has air in the middle of it. That 
water will form a sudden hollow in its bank of earth which strikes within 
equal angles at any object that projects from this bank. The rain that 
parts from the cloud does not all fall on the earth: this is due to its friction 
with the air that it penetrates, because in the course of this friction it 
becomes consumed either altogether or in great part and pours itself into 
the above-mentioned air; and often one sees the clouds descend towards 
the earth and immediately become cut short in the manner of a horse’s 
tail and remain invisible; and they are changed into wind. 

Where the straight course of the water is impeded, there sudden 
depth will be produced. This occurs because when the course of the 
water is impeded it is making percussion against an obstacle that im- 
pedes it, and because no movable thing can immediately end and con- 
sume its impetus, but it must be retained by the body which it penetrates; 
and also it does not end in this immediately after the percussion, seeing 
that every percussion is made upon the surfaces of the bodies which are 
struck; therefore, the penetration of movable things within their objects 
is a consequence born after their percussion, in which the impetus of the 
movement is consumed. 

The penetration of the movable things within their objects will be 
of as much less length than their reflex movement made in the same space 
of the falling movement, as the thing penetrated is thicker than the 




medium, where this reflex movement is made. Now the water when its 
straight movement is impeded strikes the object that impedes it, and 
immediately, not being able to penetrate it, is reflected at almost equal 
angles; after which percussion it divides and escapes by different lines 
from the spot where it struck; of these that which raises itself in the air 
acquires weight, and falls back and penetrates the other water as a heavy 
thing; after which it strikes and consumes the bed of the river; but in the 
process of penetration it is struck by the water which flows beneath its 
surface, and from stage to stage is driven back in threefold movement 
towards the place where it first struck. 

There are three positions of the movement that the water makes on 
being reflected from its percussion within the water penetrated by it: the 
first movement is towards the bed of the water; the second is towards 
the place where the water is moving; the third is whirling move- 
ment after the manner of a screw, boring continually the bank and 
the bed on which it rubs, and always gathering fresh force from the 
water that follows in succession, thrown back from the bank, which 
descends upon it from the air, and resubmerges it anew with itself 
at the bottom. 

Here then is a percussion, and the movable thing after having struck the 
object remains in the position where it was when it made the percussion; 
and the object struck follows the same line and extent of the course 
of which the striker was deprived. This happens because in this instance 
the weights are equal in size, weight and substance, and to the weight of 
the movable thing has been joined the power of the impetus of which 
the object was deprived, and it only rested with its natural weight; this 
is so, because no impetus is consumed immediately, and because the 
body that strikes is accustomed to make the reflex movement when it 
finds an object that offers resistance; but here reflex movement is not 
produced, because the object immediately flies away, bearing with it the 
power and impetus of its striker; and because always the movable thing, 
which does not attach itself to its object, is accustomed to finish the re- 
mainder of its destined movement in the reflex movement, which starts 
immediately it has finished its percussion. Here they do not become 
fixed, because they are of spherical body and of equal substance. It does 
not advance farther because it has exhausted its impetus in its percussion, 
and has given it to the object struck; it does not spring back, for it has 
nothing to serye as a foundation for it§ spring, after the manner of a 


man who wishes to jump from a board which is placed on the pavement 
on top of several pieces of a beam which has been sawn up; for as he 
gathers impetus for the leap, this impetus communicates itself to and 
unites with the board which flies away as though upon wheels; and he 
who would fain leap deprived of the impetus of the leap, is left in the 
same position in which he was when he formed the intention of leaping; 
so that from this we may conclude that the impetus can be immediately 
separated from the body where it was created and pour itself into the 
object which it has struck. 

But if the body struck be lighter than its striker, the length of the 
movement destined for this striker will be as much shorter as the impetus 
which is divided from it, attaching itself to the body struck, is diminished. 
That is, if the body struck was a pound and the striker two pounds, I 
affirm that the percussion will take away half the impetus and the move- 
ment of its striker, and the body struck having only half the power of 
impetus will take a medium course, but so much more than that made 
by the striker which follows it as it is lighter than it, and there is less 
resistance of air; excepting the power of the resistance of the air which is 
measured by drawing the same movable thing with double power; and 
if the movements are not of double length, that which is lacking has 
been taken away from them by the resistance of the air, which may be 
said to resist in the same proportion as the aforesaid movable thing is 
lacking in movement when driven by double the power there was at first. 
And if the object struck was much lighter than the striker, the air will 
offer much resistance to the movement of the body struck. And if the 
body struck is double the body that strikes it, its movement will be in 
the sub-duplicate ratio of the reflex movement of its striker. And if the 

bodies which strike are equal and similar and of equal movement and 
power, then their reflex movements will be equal in length and power, 
if the movement of similar and equal bodies be unequal then 


their reflex movement will be unequal. 


29 I 


It often happens that when one wind meets another at an obtuse 
angle, these same winds circle round together and twine themselves 
together into the shape of a huge column, and becoming thus condensed 
the air acquires weight. I once saw such a hollow column assume the 




shape of a man above the sand of the sea shore, where these winds were 
ranging round together and digging stones of a considerable size from 
this hollow, and carrying sand and seaweed through the air for the space 
of a mile and dropping them in the water, whirling them round and 
transforming them to a dense column which formed dark thick clouds 
at its upper extremity; and beyond the summits of the mountains these 
clouds were scattered and followed the direct course of the wind when 
it was no longer impeded by the mountains. 

[Of the movement of water\ 

That thing is lower which is nearer to the centre of the earth; there- 
fore that will be higher which is more remote from this centre. 

Every quantity of water will move towards its lower extremity; and 
where these extremities are of equal height, this water will not in itself 
have any movement. 

Here it is proved by these two propositions that the waters of the 
seas which are contingent will never of themselves have movement; and 
how of necessity they are of spherical surface. 

Therefore water that moves of itself has one of its extremities lower 
than the others; and that whjch does not move is of the same height in 
its extremities. 

A corollary follows which says that water does not move of itself 
unless it descends. 

Leic. 30 V. 

The variety of the positions and rates of speed pf the waters within 
their rivers is caused by the variety of the slant of their bed. The variety 
of the slant of the beds of rivers is caused by the variety of the swiftness 
of the current of the waters. 

Water of itself does not move unless the slant of the bed draws it to 
itself: what therefore was the cause of this slant of the bed different from 
its first general slant? For I allow myself to understand that the 
movements more or less of the waters in the rivers were caused only 
by the greater and less slants of the beds, as I have set forth above. 

And if the first bed of the river was formed with uniform width, slant 
and straightness, what was the cause of the varying of such conditions as 
regards the bed? For it is here shown that the water which moves above 
them must of necessity be of uniform current. The matter which makes 
the water of the rivers turbid is that which after being carried some 



distance settles upon their beds, and raises them, and changes the slant 
of the bed; and in this way it causes the variation in the courses of the 
waters. And from this we conclude that the water is the cause of 
the variation of its bed, and that the bed then of necessity changes the 
courses of the waters in greater or less speed; which variety of courses is 
then the most powerful cause of varying all the bed of its river; and so it 
is concluded: — The bed of the rivers is varied by the matter that the 
course of the water deposits there ; and the variety in the course of the 
waters is further varied by the irregularity in the bed of the river. 

A drop of water that falls in a place of uniform density and 
smoothness will splash in such a way that the edges of its mark will be 
at an equal distance from its circumference; and so conversely if it 
should not fall in a level place. Leic. 33 r. 

The centres of the sphericity of water are two: the one is of the 
universal watery sphere, the other of the particular. 

That of the universal is that which serves for all the waters that are 
without movement, which are in themselves in great quantity such as 
canals, ditches, ponds, fountains, wells, stagnant rivers, lakes, marshes, 
swamps and seas; for these although of different depth in themselves 
have the boundaries of their surfaces equidistant from the centre of the 
world, as are the lakes situated at the tops of high mountains, as above 
Pietra Pana and the lake of the Sybil at Norcia, and all the lakes which 
form the sources of great rivers, as the Ticino from Lake Maggiore; the 
Adda from Lake Como; the Mincio from Lake Garda; and the Rhine 
from Lake Constance and Coire, and from the lake of Lucerne; and as 
Trigon which passes through Africa Minor, which carries with it the water 
of three swamps at different altitudes one after another: of which the 
highest is Munace, the middle one is Pallas and the lowest is Triton. 
Again, the Nile has its source in three very high lakes in Ethiopia: it 
runs to the north and discharges itself into the Egyptian sea with a 
course of four thousand miles, and its shortest and most direct line 
which is known measures three thousand miles; it issues forth from the 
Mountains of the Moon from divers and unknown beginnings; and 
comes upon the said lakes high above the watery sphere at an altitude of 
about four thousand braccia, that is a mile and a third, in order to allow 
for the Nile falling a braccio in every mile. And the Rhone issues from 
the lake of Geneva and flows first west then south with a course of four 
hundred miles, and empties its waters in the Mediterranean sea, 



The centre of a particular sphere of water is that which occurs in the 
tiniest particles of dew, which are seen in perfect roundness clustering 
upon the leaves of the plants on which it falls; it is of such lightness that it 
does not flatten itself upon the spot on which it rests, and it is almost 
supported by the atmosphere that surrounds it, so that it does not itself 
exert any pressure or form any foundation; and for thi& reason its surface 
is drawn to itself equally from every side with equal force; and so each 
part runs to meet another with equal force, and they become magnets 
one of another, with the result that of necessity each becomes of perfect 
roundness, forming its centre therefore in the middle at an equal distance 
from each point of its surface, and being pulled asunder equally by each 
part of its gravity, always placing itself in the middle between opposite 
parts of equal weight. But as the weight of this particle of water comes 
to be increased, the centre of the curved surface immediately emerges 
from this portion of water, and makes its way towards the centre of the 
common sphere of the water; and the more the weight of this drop 
increases the nearer the centre of the said curve approaches towards the 

centre of the earth. _ . 

Leic. 34 V. 

I have seen in the case of two small canals each of a breadth of two 
braccia, which serve as a line of demarcation between the road and the 
estates, how their waters clashed together with unequal force, and then 
united, and bent at a right angle, and passed underneath a small bridge 
by this road and continued their course. But what I want to refer to in 
them is the fact that they formed there a flow and ebb, with a height of a 
quarter of a braccio, caused, now by one, now by the other canal, as will 
be stated. The first canal, being the more powerful, subdued the onrush 
of the water of the opposite canal, and by adding to it from the opposite 
direction caused it to swell up; and then the water coming above this 
from the swollen river, rose up in such a way as to acquire so much 
weight from the more sluggish water that it overcame the impetus and 
power of the water which at first was more powerful, and so drove it 
back with great fury; and consequently the victor, redoubling the 
impetus of its movement, entered with an undulation extending over 
more than a hundred feet into the more powerful canal, which at that 
time retarded and held up such of its waters as were at the boundary of 
the conquering wave. And from this wave upwards the river massed 
together so much water that after the end of the aforesaid impetus of the 
■■ 129 ■ 


wave, these waters gained the victory and drove back the first waters; 
and so they continued in succession, without ever retarding the move- 
ment of that third canal in which they were united under the aforesaid 

For this canal had four different movements, of which the first and 
second were with greater or less current, and the others according as it 
varied from the right to the left bank. The variation from the greater 
to the less current occurred when one of the streams of water made itself 
victor over the other, for as this other is turned back together with that 
which drives it an abundance of water is created under the bridge. The 
fall of the water under this bridge took place when the one stream of 
water which conquered the other had almost consumed its impetus and 
the opposing stream was left with its force already exhausted; the water 
under the bridge was then extremely low. The changing across of the 
current from the right to the left bank occurred when the water on the 
right or the left was victor, that is when the water on the right was victor 
the current struck against the left bank, and when the current in the 
canal on the left was victor it struck upon the right bank underneath the 
aforesaid bridge. 

And if this ebb and flow created within so small a quantity of water 
has a variation of a quarter of a braccio, what will it be in the great 
channels of the seas which are shut in between the islands and the main- 

It will be so much the more in proportion as its waters are greater. 

Leic. 35 r. 

O F T H E W A V E S O F W A T E R 

The wave of water created by the wind is slower than the wind that 
moves it, and swifter than the current of the water that produces the 
wind ; of this there is an example in the waves of the meadows. 

The wave of the water created by the descent of the rivers is slower 
than the current of the water that produces it; and this happens because 
the wave in such rivers is formed from the bottom of this river, or from 
its sides, and it stands as firm as is the firmness of the object that produces 
it, while the water, which continually forms itself into a wave, is con- 
tinually escaping from this wave. 

There are many occasions when the wave of the water and that of 
the wind have the same course; and many occasions when they are con- 
trary, intersecting at right angles or often at acute angles, 



The movement of the falling wave penetrates into the movement of 
the wave recoiling. The wave of the water in a circular vessel runs from 
the edge to the centre and is then bent back from the centre to the edge 
and from the edge to the centre; and so it continues in succession. 

The wave of a triangular vessel, or a vessel with sides, has not uni- 
formity of time, because its sides and angles are not equidistant from the 
centre of the vessel. 

The circle of the wave made by an object in running water will be 
oval in shape. ^ ^ 



‘To make water rise and remain upon the ascent.’ 

\With drawing of pump\ 

For the bath of the duchess Isabella; a Spring. 

Made for the stove or bath of the duchess Isabella; a is in this 
position because the screw does not turn with its socket, ^ ^ 104 r. b 

\JVith drawings^ 

Water raised by the force of the wind. 

This syringe has to have two valves, one to the pipe which draws 
the water and the other to that which ejects it. 

Method of making water rise to a height. 

In this way one will make water rise through the whole house by 
means of conduit pipes. ^ 386 r. b 



If you should wish to know what the fall of a river is in each mile 
without employing any other instrument for observing levels, you should 
follow this method: — Be careful to choose a part of the river which has 
the most conformity with the general range of the course of which you 
wish to know the fall, and take in it a hundred braccia of bank of which 
the beginning and the end are marked by two rods, as is shown above 
in ^ and at the beginning a launch a bladder, oak-apple, or small piece of 
cork, and observe how many beats of time the aforesaid object travelling 
with the descending wave takes to arrive at the end of the journey of the 
hundred braccia, and then measure many other courses, some slower and 
some more rapid, and afterwards measure the fall of the hundred 
braccia with the instrument for observing levels. And by this process, 
having measured different reaches of the water, you will then know how 
to speak only for over a hundred paces of a bank; and by observing how 
many beats of time your oak-apple has taken to traverse this course you 
will be able to calculate the fall that it makes per mile. ^ 

\With drawing of apparatus for raising water\ 

If you wish to make water rise a mile and to cause it to rest upon a 
mountain do as is represented above. And if you wish the stream of 


water to be as big as your leg make the conduit as big as your thigh. And 
if it is to rise a mile make it also descend two miles, and then the violence 
of the water which is found between b and c will be so great that it will 
draw up the water which is found md e and will turn the wheel of the 
water pump. And you must know that no air can enter into the water 
chamber by the water pump, seeing that every time that the screw of the 
water pump turns back, the valve which is at the bottom of the reservoir 
closes, and even if it were not so well stopped up it could not admit the 
air because it finds itself two braccia under water, and consequently could 
not admit air unless it first admit the two braccia of water. When you 
wish to fill the conduit you must first of all have a small lake filled with 
rains, and stop up with clay the pipes at the base of it, that is at c and e, 
and then let this lake discharge itself into the conduit. When the water 
has risen half a braccio up the wheel close the box tightly and then at the 
same time unstop the conduit at its base in c and make the wheel four 
braccia. . 

B 20 r. 

[Drawing of machine^ 

To raise water. 

, , B 54 r. 

[Hydraulic machine\ 

If twelve ounces of water produce thirty thousand revolutions of a 
machine in an hour we believe that twenty-four ounces will produce 
sixty thousand revolutions per hour of the same machine if it has the 
same fall, and that the output will be double what it was at first. 

H 90 [42] V. 



Let ^2: ^ be stagnant water, let a cht 2. screw which is turned by the 
distaff z, and the said screw carries the water into the chamber cf and 
from the said chamber a siphon tube proceeds which carries the water 
to another chamber which is round the centre of the wheel of the first 
movement, and from there the eight spokes take the water, which after 
it has fulfilled its function falls back to the spot from whence it started. 

Forster i 41 r. 


a the instrument above: 

m keeps c unstopped as long as it falls, and when 722 departs c closes, and 



when m comes to the bottom s goes to the top and draws after it the 
water of the well. 

Forster i 41 v. 


The water after issuing from the pump runs by the line a c, and 
pauses at r, and there makes counterpoise and falls down together with 
the lever n m, and draws up fresh water, of which part goes in counter- 
poise and part remains up by the line bf. 

The water departs from the centre a and flows in b, and from b as 
far as c it makes a level lever, and from c it rises by the wheel of the 
screw gently and returns to the centre c\ and make it with sixteen spokes. 

Let a bh^ the level of the earth, p is the lever of q is that of n, and 
thus first one then the other after the manner of bellows perform their 

This as far as relates to the cause of its movement has similarity with 
that above, and it varies only in that screw in the centre which conducts 
the water upwards. 

^ x'orster i 42 r. 


Here the water having ascended by the screw will arrive by the 
pipe s at the point a, and from ^ ^ it will make equidistant lever, and 
from b n will return to the first screw, and will always repeat the same 
process, and above all it makes it wider at the end than at the beginning. 

The screw a gives the water to the screw b^ and the screw b gives 
movement with the same water to the screw a, ^ 

roister i 42 v. 

[With drawings] 

The water that falls from the mouth g comes from the chamber f 
pressed by the lead d^ and when the chamber /is empty the water will 
be raised into the chamber ahj 2. valve which opens inwards. Conse- 
quently as the part below becomes lighter and the part above heavier it 
suddenly turns right over and the lead c presses the chamber a and so it 
is always in motion. ■c 

^ Forster I 45 v. 

The left chamber sends its water from y in b and in this b there is a 
valve opening inwards, by means of which the chamber c b a comes to 
be filled, and the air escapes hy a n\ but make the mouth a higher than 
the other part so that the water may not pour out. The chamber d will 


be full of air and the part e will be lead. When the chamber a b c shall 
be full it will turn right over and the lead will remain above and will 
press the water on the left, and by the time that the water has made its 
exit the lead will have gone below and the chamber will receive the 
water from the right through m s. ^ 

\With drawmgs\ 

To make water rise and remain upon the ascent. Forster i 50 v. 

This water rises by way of a pump, and after issuing forth at the 
extremity of this pump it runs by the lever from x ^ and from/^, and 
having arrived at the extremity of the said lever the water that follows 
creates counterpoise. Forster i sir. 

The water rises by the screw a b and falls in the chamber c, and from 
there it is drawn off by the siphon b f and carried into the chamber p, and 
from there until counterpoise is made in r, and then it falls into the 
stagnant water below. 

This wheel with the lever a n will turn and draw the water with the 
circle. But see that when the buckets are ten you make twelve of the 
lever and one of the counterlever. 

Forster i 5 1 v. 


[Plan on which are the words Florence^ Prato, Pistoia, Serravalle, Lago, 

Lucca, Pisal 

Let sluices be constructed in the Val di Chiana at Arezzo, so that in 
summer when there is a shortage of water in the Arno the canal will not 
become dried up, and let this canal be twenty braccia wide at the bottom 
and thirty at the surface and the general level two braccia or four, because 
two of these braccia serve the mills and the meadows. This will fertilise 
the country, and Prato, Pistoia and Pisa, together with Florence will have 
a yearly revenue of more than two hundred thousand ducats, and they 
will supply labour and money for this useful work, and the Lucchesi 
likewise. Since the Lago di Sesto will be navigable make it pass by way 
of Prato and Pistoia and cut through at Serravalle and go out into the 
lake, for then there will be no need of locks or supports, which are 
permanent but require a constant supply of labour to work them and to 
maintain them, . , 

C.A. 46 r. b 

And know that this canal cannot be dug for less than four denari 
per braccio, paying each labourer at the rate of four soldi per day. And 
the time of construction of the canal should be between the middle of 
March and the middle of June, because the peasants are not then 
occupied with their ordinary work, and the days are long and the heat 
does not prove exhausting. c a 46 V a 

[Plan of canal ascending hill by means of locksi 
[Below: 10 braccia deep and % wide^ 

Every large river may be led up the highest mountains on the 
principle of the siphon. 

If the river c d b sends out a branch at the point a and it falls back 
again at the point b, the line a b will have so much greater pressure than 
the line a c that it will be able to take away so much of it as will serve to 
lead ships up mountains. ca io 8 v a 

If a canal of water passes beneath another river with a bend like that 
of a knee, it exerts pressure in its desire to lift the cover of its conduit, 

■' -HI- ^ 


Now I ask what weight is required to resist the weight of the water that 
wishes to proceed in its course. ca 199 V b 


In order to enable each large river to maintain itself within its banks, 
it is necessary for an official to be appointed with authority to com- 
mand the people who live near to it, and so to effect repairs whenever it 
has burst its banks. 


The river which has the straightest course will best keep within its 


A trabocco is four braccia, and a mile is three thousand of these 
braccia, and the braccio^ is divided into twelve inches . . . and the water 
of the canals has a fall of two inches in every hundred trabocchi. 
Therefore fourteen inches of fall are necessary in two thousand eight 
hundred braccia of movement of the said canals. It follows that fifteen 
inches of fall give the necessary momentum to the current of the water 
of the said canals, that is one and a half braccio to the mile; and by this 
we may conclude that the water which is taken from the river of Ville- 
franche and is lent to the river of Romorantin would require ... 

. Where by reason of its lowness a river cannot enter into another it is 
necessary to raise it by a dam to such a height that it can descend into 
the one which was the higher at first. 

From Romorantin as far as the bridge at Saudre it is called the 
Saudre; and from that bridge as far as Tours it is called the Cher. 

\Map of rivers\ Mon Ricardo. Romorantin. Tours. Amboise. Blois. 

You will make a test of the level of that canal which is to lead from 
the Loire to Romorantin by means of a channel one braccio wide and 
one braccio deep. 

[Map of riversl Era (Loire). Scier (Cher). Villefranche. Bridge of 
Saudre. Saudre. Ship. 

On the Eve of Sant* Antonio I returned from Romorantin to 
Amboise, and the King [of France]® departed two days before from 
Romorantin. c.a. 336 V. b 

^ Braccio - nearly two English feet. ® MS. di fr an crossed out, 


The canals of Milan have a fall of one braccio or thereabouts in every 
mile. And an inch a mile is found sufficient in respect to the surface 
movement of the water. 

Moreover reckoning a fall of a braccio in every mile, in a space of 
four hundred miles it would become necessary for the water to turn back, 
because the world .. . 

C.A. 352 V. a 

Let the Guild of the Wool Merchants construct the canal and take 
the receipts, making the canal pass by way of Prato, Pistoia, Serravalle 
and empty itself into the lake; and it will be without locks and more 
permanent and will produce more revenue from the places through 
which it passes. _ 

c,A. 398 r. a 

The roots of the willows do not suffer the banks of the canals to be 
destroyed; and the branches of the willows, nourished during their 
passage through the thickness of the bank and then cut low, thicken 
every year and make shoots continually, and so you have a bank that has 
life and is of one substance. 

When the pool that is [provided] for the month of June is empty, 
stop up the mouths and bend the river which has poured itself into it, 
and give it its outlet in the fall of the mill. 

^ F 1 3 r. 

Make a lock to the narrow canal that comes from the sea, in order to 
be able to close it against storms and the tide and to open it at the ebb. 

F 16 X. ■ 


Make this in the book of the aids, and in order to prove it cite the 
propositions that have been proved. And this is the true order, because 
if you wished to supply a help to each proposition it would still be neces- 
sary for you to make new instruments in order to prove this utility; and 
by so doing you would confuse the order of the forty books and so also 
the order of the figures; thus you would have to blend practice with 
theory, which would cause confusion and lack of continuity. ^ ^ 

A great weight may be deposited upon a ship without the use of 
windlasses, levers, ropes, or any force: 

In order to deposit each very heavy weight that is all in one piece 


upon a floating barge, it is necessary to draw this weight to the shore of 
the sea, setting it lengthwise to the sea at the edge of the shore. Then a 
canal should be made to pass beneath this weight and to project as far 
beyond it as the half of the length of the barge which is to carry 
this weight; and in like manner the width of this canal should be 
regulated by the width of the barge, which should be filled with water and 
drawn beneath the weight. And then after the water has been baled out 
the ship will rise to such a height as to raise the said weight from the 
ground of itself. Thus laden you will then be able to draw it to the sea 
and lead it to the place that is prepared for it. ^ ^ 


By the making of the Martesana canal the amount of water in the 
Adda is lessened owing to it being distributed over many districts in 
order to supply the meadows. A remedy for this would be to make many 
small channels because the water which has been drunk up by the earth 
does no service to anyone, nor any injury because it has been taken from 
no one; and by the construction of such channels the water which before 
was lost returns again and is once more of service and use to mankind. 
And unless such channels have first been constructed it is not possible to 
make these runlets in the lower-lying country. We should say therefore 
that if such channels are made in the Martesana, the same water, drunk in 
by the soil of the meadows, will be sent back upon the other meadows by 
means of runlets, this being water which had previously disappeared ; 
and if there were a scarcity of water at Ghiara d’Adda and in the Mucca 
and the inhabitants were able to make these channels it would be seen that 

the same water drunk in by the meadows serves several times for this 


F 76 V. 


It is possible that in a canal concave in its length the water flows 
with uniform depth. 

It is impossible for the water in a convex canal to flow with uniform 
volume although the canal is of uniform width. 

° F 88 V. 


A fall of two inches every hundred trabocchi, and these hundred 
trabocchi are four hundred and fifty braccia. 

144 - 


The greatest depth of the rivers will be beyond the current where the 
water is at rest. 

H 6s [17] r. 

The more the water falls, the more it leaps. 

On the second day of February, 1494, at the Sforzesca I have drawn 

twenty-five steps, each of two thirds of a bracdo high and eight braccia 
wide. o to 

The greatest depth of water will be between the percussion and 
the gurglings which result from it. 

H65 [17] V. 

No sluice should be narrower than the general width of the canal 
because the water in this event forms eddies and breaks the bank. ' 

rm • r H 76 [28] V. 

[Estimate for canaf\ 

The canal which is sixteen braccia in width at the bottom and twenty 
at the top may be said to average eighteen bracda over its whole width - 
and if it is four bracda in depth and costs four denari per square bracdo 
It will cost per mile for excavation alone nine hundred ducats, the square 

braccio being calculated in ordinary braccia. 

But if the braccia are such as are used to measure land, of which every 
four are four and a half, and if the imle consists of three thousand ordinary 
braccia and these are converted into those used to measure land, then 
these three thousand braccia lose a quarter so that there remain two 
thousand two hundred and fifty braccia; and therefore at four denari the 
braccio the mile comes out at six hundred and seventy five ducats; at 
three denari per square braccio the mile works out at five hundred and 
six and a quarter ducats, and therefore the excavation of thirty miles of 
the canal will work out at fifteen thousand one hundred and eighty 
seven and a half ducats. ^ ' 

H 91 [43] r. 

The water that falls over its embankments lays them bare and breaks 
them down on the opposite side. 


G A R D E N O F B L O I S 

[With diagram'l 

a bi% the conduit of Blois, made in France by Fra Giocondo; ^ ^ is 
what is lacking in the height of this conduit; is the height of the 



garden of Blois; ^/is the fall of the siphon b c e f\f g is where this 
siphon discharges into the river, " ^ ^ 


\With drawing 

To ensure that the mouths of the canals which hollow themselves out 
from the rivers do not become filled up with shingle, and also to prevent 
the shingle from remaining in the middle of the dam that has been 
constructed against it, it should be made with a transverse descent. 

K loi [21] r. 

\Canal of the Ticmo\ 


The declivity of the canal with the small outlets at its bottom. 

All the water ^ ^ is that which enters into the canal having outlet 
through the openings placed at the bottom; and all the water a ch that 
which enters in the canal having the openings near the surface of the 
water. The water c b having no outlet does not move its mass, and not 
moving it does not enter into the other mass but [this other] will go into 
the Ticino. 

And in order thus to raise the openings make the course of the 

water more [less?] slanting, and make the course slower in consequence. 

Then this course in the same time draws a less quantity of water in the 

canal, and the mills receive less than at first although they receive the 

whole of it, and the outlets become full of impurities and choked up. 

However I shall maintain the water in the canal at a height of one 

braccio and a half as at first, and the outlets at the bottom as at first, and 

I shall let in the water by degrees, r , , _ . ot 

JO K 109 [29-30] r. and 108 [28] v. 

[Notes with drawing of section of Loire] 


The river is higher behind the bank b d than beyond this bank. 
Island where there is a part of Amboise. 

The river Loire which passes by Amboise passes hj a bc d^ and after 

^ This technical note as to the work of the Veronese architect Fra Giocondo in the 
garden of the ch§.teau of Blois was most probably written by Leonardo while at Milan 
during the French occupation, the information having been supplied him by some member 
of the French court. 



passing the bridge c d ^ doubles back on its course by the canal de bf, 
in contact with the embankment d b which comes between the two 
opposite movements of the above-mentioned river a be d,de bf. Then 
it turns back by the canal// g h n m reunites with the river from 
which it was formerly divided, which passes hj kn and makes k m r t. 
But when the river is swollen it then runs all in one direction, passing the 
embankment b d. 

B.M. 269 r. 

[French canal —project\ 

The main channel of the river does not take the turbid water, but 
this water runs in ditches on the outside of the town with four mills at 
the entrance and four at the exit; and this will be constructed by 
damming the water above, at Romorantin. 

The water may be dammed up above the level of Romorantin at 
such a height that it works many mills in its descent. 

The river at Villefranche may be led to Romorantin, and this may 
be done by the people who live there, and the timbers which form their 
houses may be taken on boats to Romorantin, and the river may be 
dammed up at such a height that the water can be led down to 
Romorantin by an easy gradient. 

[Sketch map of Loire with tributaries^ 

If the river m n^ 2 l tributary of the river Loire, were turned into the 
river of Romorantin with its turbid waters it would enrich the lands that 
it irrigated and make the country fertile, so that it would supply food for 
the inhabitants and it would also serve as a navigable canal for purposes 
of commerce. 


By the ninth of the third: that which is swifter consumes its own bed 
more, and conversely the water that is slower leaves more behind of that 
which causes it to be turbid. 

Therefore when the rivers are in spate you ought to open the flood- 
gates of the mills so that the whole course of the river may . . . there 
should be many floodgates for each mill so that . . . may open and give 
a greater impetus and thus the whole bed will be scoured. 

And let the sluice be made movable like the one that I devised in 
Friuli, where when the floodgate was open the water which issued forth 


from it hollowed out the bottom; and below the two sites of the mills 
there should be one of these floodgates, one with movable sluices 
being placed below each of the mills. b m 270 v 

Here there are, my lord, many gentlemen who will undertake this 
expense between them, if so be that they are allowed to enjoy the use of 
the waters, the mills and the passage of ships; and when the price shall 
have been repaid them they will give back the canal of the Martesana. 

Forster iii 1 5 r. 

That a river which has to be diverted from one place to another 
ought to be coaxed and not coerced with violence; and in order to do 
this it is necessary to build a sort of dam projecting into the river and 
then to throw another one below it projecting farther; and by proceed-* 
ing in this way with a third, a fourth, and a fifth, the river will discharge 
itself in the channel allotted to it, or by this means it may be turned away 
from the place where it has caused damage, as happened in Flanders 
according to what I was told by Niccolo di Forzore. 

\ drawingl How one ought to repair by means of a screen a 
bank struck by the water, as below the island of Cocomeri. ^ 


No canal which issues forth from rivers will be permanent unless the 
water of the river from which it has its origin is entirely closed up, as is 
the case with the canal of Martesana and that which issues from the 

The canals ought always to be provided with sluices, so that excessive 
floods may not damage or destroy the bank and the water may always 
maintain itself in the same volume. t „ 

Leic. 1 8 r. 

How in order to twist the line of the water one should make a twist 
in the line of the bank with a few stones: By the fourth of the second, 
where it was proved that the line of the water of the rivers was a con- 
course of the reflex movements of the water that has struck upon its 
banks, and has there multiplied and raised itself and hollowed out its bed 
beneath itself. And this is what would occur if anyone set out to twist 
the bank when the river a certain space above had shown that it wished 
to bend, and then had not continued this bending process, and you were 
to follow it up again gradually and minister to its first desire with an 



almost imperceptible curve; and thus you will proceed to make your 
attempt. But if you should try to bend the water in the direct line of its 
strength all your work will be in vain, because it will break every ob- 
stacle. And if with your lock you raise the level of the water so high that 
it swallows up so much in itself that the current loses its impetus in the 
expanse of water that has been formed, this can have a good result, and, 
by the fifth of the first, it will fill up all its bed with mud. But make it so 
that the water does not run along the bank. ^ . 

Leic. 27 V. 

[Of dinjerting a river and protecting a house^ 

I have a house upon the bank of the river, and the water is carrying 
off the soil beneath it and is about to make it fall in ruin; consequently I 
wish to act in such a way that the river may fill me up again the cavity 
it has already made, and strengthen the said house for me. In a case 
such as this we are governed by the fourth of the second, which proves 
that The impetus of every movable thing pursues its course by the line 
along which it was created’; for which reason we shall make a barrier at 
the slant n m, but it would be better to take it higher up at 0 /, so that 
all the material from your side of the hump might be deposited in the 
hollow where your house is; and the material from the hump k would 
then do the same, so that it would serve the need in the same winter. 
But if the river were great and powerful the said barrier would have to 
be made in three or four attempts, the first of which, made in the direc- 
tion that the water is approaching, ought to project beyond its bank a 
fourth part of the width of the river; then, below this, you should make 
another, distant as far as the summit of the leap that the water makes 
when it falls from the first barrier, •— for in this summit of its leap the 
water leaves the summit of the mound made by the shingle which was 
hollowed out by the first percussion, made by the water when it fell 
from the first barrier upon its bed. And this second dam extends halfway 
across the breadth of the river. The third should follow below this, 
starting from the same bank, and at the same fixed distance from the 
second as the second was from the first; and it follows its length as far 
as three-quarters of the width of the river. And so you will proceed 
with the fourth dam which will close the whole river across. And from 
these four dams or barriers there will result much greater power than if 
all this material had been formed into one barrier, which in uniform 
thickness would have closed the whole width of the stream. And this 



happens by the fifth of the second, where it is proved that the material 
of one single support, if it be quadrupled in length, will not support the 
fourth of that which it used formerly to support, but much less. 

I find that the water, that falls at the foot of the dams of rivers, places 
material towards the approach of the water, and carries away from the 
foot of the dam all the material on which it strikes as it falls. Now I could 
wish that it would place the material where it falls, and thereby bank up 
and fortify this dam: which thing might be done in this way — 

Leie. 32 r. 



‘Take away that yellow surface which covers the 
orange and distil it in a retort until the extract 
is pronounced perfect.’ 


If you place your second finger under the tip of the third in such a 
way that the whole of the nail is visible on the far side, then anything 
that is touched by these two fingers will seem double, provided that the 
object touched is round. 

C.A. 204 V. a 

I take a vessel filled with wine and I draw off the half and fill it up 
again with water: in consequence the vessel will contain half wine and 
half water. 

Then I draw off half again and then fill up with water, wherefore 
there remains ... 

Since every continuous quantity is divisible to infinity, if a quantity of 
wine be placed in a vessel through which water is continually passing it 
will never come about that the water which is in the vessel will be without 


If you wish to find the part of the magnet that naturally turns to- 
wards the north get a large tub and fill it with water; and in this water 
place a wooden cup and set in it the magnet without any more water. It 
will remain floating in the manner of a boat, and by virtue of its power 
of attraction it will immediately move in the direction of the north star; 
and it will move towards this, first turning itself with the cup in such a 
way that it is turned towards this star, and will then move through the 
water and touch the edge of the tub with its north side, as before 

[JVit/i drawing] 

This globe should be a half or a third of a braccio in diameter; and it 
should be of clear glass and filled with clear water with a lamp in the 
middle, with the light in about the centre of the globe, and when 
suspended in the centre of a room it will give a great light. 

[Sphericity of water. Experiment] 

A drop of dew with its perfect round affords us an opportunity of 
considering some of the varied functions of the watery sphere; how it 


contains within itself the body of the earth without the destruction of the 
sphericity of its surface. For if first you take a cube of lead of the size 
of a grain of millet, and by means of a very fine thread attached to it 
you submerge it in this drop, you will perceive that the drop will not 
lose any of its first roundness, although it has been increased by an 
amount equal to the size of the cube which has been shut within it. 

F 62 V. 

[Light and heat. Sun and mirrors\ 

Whether the greater light with less heat causes concave mirrors to 
reflect rays of more powerful heat than a body of greater heat and less 

For such an experiment a lump of copper should be heated and 
placed so that it may be seen through a round hole, which in size and 
distance from the mirror is equal to the heated copper. 

You will thus have two bodies equal in distance but differing in heat 
and differing in radiance, and you will find that the greater heat will 
produce a reflection of greater heat in the mirror than the aforesaid flame. 

We may say therefore that it is not the brightness of the sun which 
warms but its natural heat. 

It is proved that the sun in its nature is warm and not cold as has 
already been stated. 

The concave mirror although cold when it receives the rays of the 
fire reflects them hotter than the fire. 

A ball of glass when filled with cold water sends out from itself rays 
caught from the fire which are even hotter than the fire. 

From the two experiments referred to, it follows, as regards this 
warmth of the rays that issue from the mirror or from the ball of cold 
water, that they are warm of their own essence, and not because the 
mirror or ball are hot. And in this case the same thing happens when the 
sun has passed through the bodies which it warms by its own essence. 
And from this it has been concluded that the sun is not hot, whilst by the 
experiments referred to it has been proved that it is extremely hot, — from 
the experiment which has been mentioned, of the mirror and of the ball 
which being cold and taking the rays of the heat of the fire convert them 
into warm rays because the primary cause is warm. And the same thing 
happens with the sun, which being itself warm, in passing through these 
cold mirrors reflects ereat heat, „ 

° F 85 V. 





You will discover the various degrees of thinness of the waters by 
suspending at a uniform depth of the opposite ends a strip of old linen 
cloth, which should be dry, and which should penetrate on each side as 
far as the bottom of two vases filled with the two different kinds of water 
with which you wish to make your experiment. Then these waters will 
rise a certain distance on the cloth and will proceed gradually to 
evaporate, and as much as has been the evaporation of that which has 
risen up, so much will it rise again from the rest until the vase is dried up. 
And if you refill the vase the water will all rise in the piece of cloth with 
imperceptible slowness, and so as has been said it will gradually become 
dried up. And by this means the piece will remain full of the rest of the 
water which has evaporated, and in this way, by means of the weights 
that have been acquired, you will be able to tell which water holds more 
earth in solution than the other. 

G 37 V. 



Since the more the water in the vessel diminishes the more its surface 
is lowered, and the more the surface of the water is lowered the less 
swiftly the siphon flows, but if the siphon descends at the same time as 
the surface of the water that supports it, without doubt the movement of 
the water which pours through will always be equal in itself, therefore 
in order to make this equality let us make the vessel n in position above 
the bath of mercury m. This vessel is a boat which supports the siphon 
which penetrates below from the air into the mercury. And this mercury 
proceeds to rise through the siphon n s t into the vessel/. And in pro- 
portion as the surface of this mercury descends so the boat which rests 
upon it descends at the same time as the siphon, which is formed of fine 
burnished copper and falls into a vessel, and this when it acquires the 
requisite weight falls and thereby creates fire by its impact. 

G 48 r. 

One may find by experiment whether if untarnishable varnish be 
melted by the fire it moves from slanting positions if it is not of great 
thickness, — this varnish after it has been liquefied should be smoothed 
constantly with a brush. 

G 73 V. 




[The flowing of liquids\ 

If a cask is filled four braccia high with wine and throws the wine a 
distance of four braccia away, when the wine has become so lowered that 
it has dropped to a height of two braccia in the cask, will it also throw the 
wine through the same pipe a distance of two braccia, that is whether the 
fall, and the range that the pipe can throw, diminish in equal proportion 
or no. 

If from the cask when full two jugs are filled through the pipe in an 
hour, when the cask is half full it ought for this reason to fill only one 
jug in an hour, if pouring from the same pipe. 

This rule with all the other similar ones about waters which are 
poured through pipes ought to be put at the commencement of the 
instruments, in order to be able through various rules the better to pro- 
ceed to the proofs of these instruments. 

[Good or poor mathematician\ 

In order to make trial of anyone and see whether he has a true judg- 
ment as to the nature of weights, ask him at what point one ought to cut 
one of the two equal arms of the balance so as to cause the part cut off, 
attached to the extremity of its remainder, to form with precision a 
counterpoise to the opposite arm. The thing is never possible, and if he 
gives you the position it is clear that he is a poor mathematician. 

M 68 V. 

Cause an hour to be divided into three thousand parts, and this you 
will do by means of a clock by making the pendulum lighter or heavier. 

B.M. 191 r. 


If you wish to make a fire which shall set a large room in a blaze 
without doing any harm you will proceed thus: first perfume the air 
with dense smoke of incense or other strongly smelling thing, then blow 
or cause to boil and reduce to steam ten pounds of brandy. 

But see that the room is closed altogether, and throw powder of 
varnish among the fumes and this powder will be found floating upon 

the fumes; then seize a torch and enter suddenly into the room and 
instantly everything will become a sheet of flame. Forster i 43 r 

Take away that yellow surface which covers the orange and distil 
it in a retort until the extract is pronounced perfect. 

■ ' . . ■ ■ ■ ■ 


Close up a room thoroughly and have a brazier of copper or iron with 
a fire in it, and sprinkle over it two pints of brandy a little at a time in 
such a way that it may be changed into smoke. Then get someone to 
come in with a light and you will see the room suddenly wrapped in 
flame as though it was a flash of lightning, and it will not do any harm to 

Forster X 44 V. 

^Experiment with waves of water and of air^ \With fi^res\ 

Place yourself in a boat and construct an enclosure n m o p and fix 
within it two pieces of board s r and t and make a blow at a and see 
whether the broken wave passes with its suitable part as far as ^ ® 

And from the result of the experiment which you make with the 
wave cut oflF by the circular wave of the water, may be inferred what 
happens with that portion of the wave of air which passes through the 
airhole through whkh the human voice passes when confined in a box; 
as I heard at Campi from a man who had been shut up in a cask with the 
bunghole left open. Quademim.^v. 

’•As figure shows, these two pieces of board are placed opposite to each other at right 
angles to the sides of the enclosure and are each about a third of its width. 

® The lines b a, c a form an acute angle with equal arms which pass through the ends 
of the two boards s r and t r and continue to the points b and c, which are near the sides of 
the enclosure. 



‘O speculators about perpetual motion, how 
many vain chimeras have you created in the like 
quest? Go and take your place with the seekers 
after gold.’ 

^With dr awing\ 

Method of drying up the marsh at Piombino. 

c.A. 139 r. c 


Here there is need of a clock to show the hours, minutes and seconds 
ore punti e minutt). 

For measuring how great a distance one goes in an hour with the 
current of the wind. 

For learning the quality and density of the air and when it will rain. 

For reckoning the mileage of the sea. 

0 0 c.A. 349 V. a 

[With drawing 

This is the way to dredge a harbour, and the plough m n will have in 
front of it spikes shaped like ploughshares and knives, and this plough 
will be used to load a large cart with mud. The cart will have its back 
perforated after the manner of a net in order that the water may not be 
shut within the box; and the said plough is to be moved along above the 
place where the mud is to be dug out, and along with it a barge; and 
when it has reached the bottom the windlass b will draw it underneath 
the windlass a^ and the windlass a will raise it up when it is full as far as 
its beam, in such a way that there will be room for the barge to go 
underneath it and take the mud from the plough; and so this plough will 
be able to dislodge the mud from the bottom and unload it upon the 
barge which is placed underneath it. cAsoyrb 

Make to-morrow out of various shapes of cardboard figures descend- 
ing through the air, falling from our jetty; and then draw the figures and 
the movements made by the descent of each, in various parts of its 

C.A. 375 r. c 

[With drawings] 

These scissors open and shut with a single movement of the hand. 

Scissors used by the bonnet-makers for cutting cloth. Rapid in the 
action of opening and shutting like the others. 

This [tool] has in itself so much more ease in its movement because the 
user does not have to adjust the spring or curve, as is the case with those 


scissors which are all in one piece. With these it is not necessary to wait 
in order to cut the threads of the cloth, or to bend by force the spring 
which is in the heel of the scissors. 

This closes at the same rate of speed as the rest ; but opens much more 

rapidly. c.A.397 v.a 

[Drawing of apparatus with ropes and pulley s\ 

Method of raising and lowering the curtains of the treasures of silver 
of the lord. ^ 

[With drawing of tube descending from surface of water to confer mouth of 
man in dicing dress\ 

This instrument is employed in the Indian Ocean in pearl fishing; it 
is made of leather with numerous rings so that the sea may not close it 
up. And the companion stands above in the boat watching, and this 
[diver] fishes for pearls and corals, and he has goggles of frosted glass and 
a cuirass with spikes set in front of it. ^ ^ g ^ 


[With drawingl 

It is necessary to have a coat made of leather with a double hem 
over the breast of the width of a finger, and double also from the girdle 
to the knee, and let the leather of which it is made be quite air-tight. 
And when you are obliged to jump into the sea, blow out the lappets of 
the coat through the hems of the breast, and then jump into the sea. 

And let yourself be carried by the waves, if there is no shore near at 
hand and you do not know the sea. 

And always keep in your mouth the end of the tube through which 
the air passes into the garment; and if once or twice it should become 
necessary for you to take a breath when the foam prevents you, draw it 
through the mouth of the tube from the air within the coat. ^ gj ^ 

[Alarum--clock'\ [With drawing\ 

A clock to be used by those who grudge the wasting of time. 

And this is how it works: — when as much water has been poured 
through the funnel into the receiver as there is in the opposite balance 
this balance rises and pours its water into the first receiver; and this 

162 ■ 


being doubled in weight jerks violently upwards the feet of the sleeper, 
who is thus awakened and goes to his work. 

° B 20 V. 

[Drilling machine] 

In order to drill through a beam it is necessary to hold it suspended 
and drill from below upwards so that the hole may empty of itself, and 
you should make this canopy so that the sawdust may not fall upon the 
head of him who turns the screw; and see that the turners rise at the 
same time as the said screw. And make the hole first with a fine auger 
and then with a larger one. 

o B 47 V. 


A sledge for use in mud. And make the part that comes upon the 
ground united in order that it may not get stuck in the mud. ^ ^ 


A sledge for use in mountainous and rocky places. And do not make 
the part that touches the ground united, so that it may be less difficult to 
drag; for the less the weight touches the less difficult it is to move. 

B 50 r. 

[Timepiece, Withdrawing] 

Four springs for a timepiece, so that when one has finished its 
course the other commences, and as the first turns the second remains 
motionless. And the first is fixed above the second like a screw, and 
when it is fixed the second spring takes the same movement completely 
and so do all. 

[Withdrawing] [Paddle-boat] 

Barge made of beams and covered over above. But make a large 
wheel of oars concealed within it, and make a furrow from one end of it 
to the other, as appears in a^ where the wheel can touch the water. 

'b 76 y. 

[To make concrete] [With drawings] 

^ is a box which can open and empty itself, and in it you can make 
a concrete formed of fine pebbles and chalk. Let these blocks dry on the 
ground and then place them one upon another under the water, in order 
to form a dam against the rush of the water. 



Frames filled with gravel and twigs of birch, that is a layer of twigs 
\sketcK\ placed vertically in this direction and a layer of gravel, then a 
layer in this contrary direction \s'ketc}i\ and then a layer of gravel, and 
thus you will construct it bit by bit. b 70 v 


See if there are a number of small stones of different sizes whether 
the heaviest goes farthest when one throws it, then try alone with the 
same instrument and force, and see whether it travels a greater or less 
distance alone than when accompanied. And whether also if the stones 
are all of the same form and weight, like the balls of an air-gun, and are 
thrown by the same force in the same time they travel the same distance. 



These bellows are like a sugar loaf and have a partition which divides 
them lengthwise in two parts. One — that is the upper part — is filled with 
water; that below is filled with air. The water falls down into the cubic 
space of the air through a small hole which is near the socket, and the 
increase of the water drives the air through the mouth of the bellows. 
Any scarcity of water in the upper part is filled by means of a valve 
which admits the air, and so also with the others; and this is the most 
serviceable type of bellows that can be used. g 

Webbed glove for swimming in the sea. \Wtth drawing 

[Water beilows\ [Drawings] 

These are kinds of bellows without leather and they are of admirable 
utility and extremely durable. And their method of use is as follows: — 
The bellows is always from the centre downwards full of water, that is 
M N, and in the continual revolution of the bellows N rises until it 
reaches the air hole S T which is made in the outside of the second 
covering, as appears in the instrument below, and comes to meet with 
the said pipe S T the hole 0 which is in the reservoir iV, and as much as 
is the volume of water that goes from iV to M so much air enters through 
the hole 0 in the reservoir N, and as much air is driven out of the reser- 
voir M zsN gives it of water. And the air which is driven out from M 
by the water is that which blows the bellows. The said bellows should 




be of oak because this resists water for the longest time, and have inside 
it a coating of turpentine and pitch, so that when it is not in use the part 
above which is out of the water does not come to open; and this type of 
bellows is turned by the weight of a man walking above on the steps. 

It would also be extremely useful to cause it to turn by the force of 
a fall of water. 

The base of the bellows below the tube S T remains fixed, and the 
rest turns there within as a case would within its cover. 

Use salt water so that it may not become foul in the bellows. 

B 82 r. 

\Wtth drawings of macMne\ 

To produce a marvellous wind. 

E 33 V. 

The current will be so much the more abundant as the small doors 
open with less descent, [discesat MS. dissci . . .) 

The whole space of the small doors is equal to the whole space of the 
width of the pipe. 



Here the calculation of the power is not at present fixed. 

But you, reader, have to understand that this has a use, which arises 
by means of the saving of time, which saving springs from the 
fact that the instrument which conveys the earth up from below is 
always in the act of carrying it and never turns back. The adversary 
says that in this case it takes as long to turn round in a useless 
circle as to turn back at the end of the forward action. But since the 
additional spaces of time that are interposed between the spaces of 
useful time are equal in this and in all other inventions, it is necessary to 
search here for a method whereby the time may be spent in as vigorous 
and effective a method of work as possible, which will be by invent- 
ing a machine that will take more earth; as will be shown on the reverse 
of this page. 

The winch n as it turns causes a small wheel to revolve, and this small 
wheel turns the cogged wheel and this wheel/is joined to the angle of 
the boxes which carry the earth from the swamp and discharge them- 
selves upon the barges. But the two cords mf and m b revolve round 



the pole/, and make the instrument move with the two barges against 

w and these cords are very useful for this purpose. 

’ Thfp^L is so made as to descend to as great a depth as the wheel 
has to descend in order to deepen the water of the marsh. ^ ^ ^ 

As the attachment of the heavy body is further from J 

the wheel the revolving movement of the wheel round p 
become more difficult although the motive power may not vary. 

The same is seen with the time of clocks, for, if you place the two 
weights nearer or farther away from the centre of the timepiece, you 
make the hours shorter or longer. f 7 v. 

cfyrtd\hickness, at the sides the twelfth part of “ mck 
This lens of crystal should be free from spots and very clear; and at the 
sides it ought to be the thickness of a twelfth of an inch, that is to say of 
the one hmdred and forty-fourth part of a braccio, and thin in the centre 
according to the sight that it ought to serve for, that is to say according 
to the proportion of those lenses which agree with it; and let it be writed 
S the^saL mould as these lenses. The width of the frame vdl be 
one sixth of a braccio and its length one quarter of a braccio; conse 
quL% it will be three inches long and two wide, that is to say a square 
Lf. And this lens should be held at a distance of a third of a 
bLcio from the eye when used, and it should be the same distance from 
iTteter that yol are reading. If it is farther away thts letter ^ 
appear larger, so Aat the ordinary type of print will seem like a letter 

TMs kM irsmLble for keeping in a cabinet; but if you wish to keep 
it outside make it one eighth of a braccio long and one twelfth wide. 

''‘Cri Ki »e go» i. h.„ tat, whjd 

constructed as you see, and place above the instrument, of which the 
centre may be upon a circular line which turns exactly five bracci , 
dileterLngoneand ibraccia. Then tightly close the instmment, 
have harmonic time, smear all the inside of the instrument with tur- 
pentine, turn the wheel uniformly and notice where the top layer ot dust 



has stuck to the turpentine, and see how many revolutions the wheel 
has made and in how many beats of harmonic time. And if the wheel 
has made two revolutions in one beat of time, which amounts to ten 
braccia, that is to say the three-hundredth part of a mile, you will be able 
to say that this instrument has moved a mile in three hundred beats of 
time, and that an hour is one thousand and eighty beats of time; which 
will make three miles an hour and one hundred and eighty three- 
hundredth parts. 

^ F 48 V. 

[jd decoration] 

If you make small pipes after the manner of goosequills, which are 
opaque and white with a coating of black within and then transparent, 
and with sardonyx outside and then transparent; and let all the thick 
portion of the pipes be made up of these mixtures, and then moisten 
them and press them and leave them to dry in the press; if you press 
them flat they will give one effect, if you press them into a rectangle they 
will give another and similarly if you press them into a triangle; but if 
you press them in front or folded in different ways you will also do well. 

And if in the transparent part exposed to the sun you make with a 
small style a mixture of different colours, especially of black and white 
opaque, and yellow of burnt orpiment, you can make very beautiful 
patterns and various small stains with lines like those of agate. 

F 55 V. 



Lamp in which as the oil becomes low the wick rises. 

And this proceeds from the fact that the wheel which raises the 
wick rests upon the oil. As the oil diminishes so the wheel descends, 
and as it descends it revolves by means of the thread that is wrapped 
round its axle, and the cogs of the wheel push the toothed pipe that 
receives the wick. 

It will also do the same if a the axle of the wheel does not descend, 
and the only descent is that of the light object b which floats upon the 
oil, for this light object descends at the same time as the surface of the 
oil, and causes the wheel to turn, and this by means of its cogs pushes up 
the aforesaid cogged pipe with a slow movement. ^ 



[With drawings^ 

This can also be made without a spring, but the screw above must 
always be joined to the part of the movable sheath. 

No coins can be considered as good which have not the rim perfect; 
and in order to ensure the rim being perfect it is necessary first that the 
coins should be absolutely round. 

In order to make this it is necessary first to make the coin perfect in 
weight, breadth and thickness; therefore you must first have many plates 
made of this [uniform] breadth and thickness drawn through the same 
press, and these should remain in the form of strips, and from these 
strips you should stamp out the round coins after the manner in which 
sieves are made for chestnuts, and these coins are then stamped in the way 
described above. 

The hollow of the mould should be uniformly and imperceptibly 
higher at the top than at the bottom. 

This cuts the coins of perfect roundness, thickness and weight, and 
saves the man who cuts and weighs, and saves also the man who makes 
the coins round. 

They pass therefore merely through the hands of the worker of the 
plate and the stamper, and they are very fine coins. ^ ^ 


Among the accidental forces of nature, percussion greatly exceeds 
each of the others created by the motive powers of heavy bodies in 
equal time with equal movement, weight and force. This percussion is 
divided into simple and compound. Simple is that in which the motive 
power which is the striker is joined with the movable thing at its j unction at 
the place struck; compound is that in which the movable thing as it strikes 
does not end its movement at the place of its impact, as does the hammer 
which strikes the die that stamps the coins. And this compound per- 
cussion is much weaker than simple percussion, for if the flat end of the 
head^ of the hammer were to attach itself to the coin which it had to 
stamp and which it had struck upon the mould where was the impression, 
so that on this flat end of the head of the hammer there had been 
engraved the relief that was on the coin in reverse, the impression would 
be more definite and clear on the side struck with simple movement than 
* MS. bocha. 


on the side where the percussion is compound ; as with the coin that remains 
struck in the die where the hammer has struck it in its descent, the per- 
cussion being reflected and thrown back against the front of the hammer, 

G 62 V. 

[Of the siphon] 

A preparation of mercury drawn through very fine copper of the 
shape of a siphon, the sides through the length of which the liquid rises 
and falls being of imperceptible thickness, will be seen to form a time- 
piece after the manner of an hourglass, and this is the slowest and most 
graduated descent that can be made, so much so that it may happen that in 
an hour not one grain of the mercury passes from one vessel to the other. 

And the surface of its container is sensitive by reason of the opacity of 
the mercury, the skin of this mercury becoming imperceptibly lowered 
with the descent that occurs as the siphon discharges itself; and by this 
means you will be able to create a fire which by means of percussion will 
generate itself at the end of a year or more, and this without any sound 
down to the moment of the creation of the fire. 

And it is shown in the margin at the foot of the fourth page (folio 
48 r.) how one ought to fix or set up this vessel, which by the power 
observed gives the result which is promised us at the end. 


The ancients have employed different methods in order to discover 
what distance a ship traverses in each hour. Among them is Vitruvius 
who expounds one in his work on architecture, but his method is falla- 
cious like the others. It consists of a wheel from a mill touching the 
ocean waves at its extremities, and by means of its complete revolutions 
describing a straight line which represents the line of the circumference 
of this wheel reduced to a condition of straightness. But this device is 
only of value on the smooth still surface of lakes; should the water move 
at the same time .as the ship with an equal movement the wheel remains 
motionless; and if the movement of the water be either more or less 
swift than that of the ship, then the wheel will not have a movement 
equal to that of the ship, so that such an invention has but little value. 

Another method may be tested by experiment over a known distance 
from one island to another, and this is by the use of a light board which is 



struck by the wind, and which comes to slant to a greater or less degree 
as the wind that strikes it is swifter or less swift, and this is in Battista 

As regards the method of Battista Alberti which is founded upon an 
experiment over a known distance from one island to another, such an 
invention will work successfully only with a ship similar to that with 
which the experiment has been tried, and it is necessary that it should be 
carried out with the same freight and the same extent of sail, and with 
the sail in the same position, and the waves of the same size. But my 
method serves with every kind of ship, whether it be with oars or sail; 
and whether it be small or large, narrow or long, high or low, it always 


[With drawing 


Show all the ways of unlocking and releasing. Put them together in 
their chapter. ^ v 


To warm the water of the stove of the duchess add three parts of 

warm water to four parts of cold water. 

r I 34 r. 

[With ground plan of Castle of Milan\ 

A way of flooding the castle. ^ ^ 


To make a beautiful garment take fine cloth and give it a strong- 
smelling coat of varnish made of oil of turpentine; and glaze it with 
eastern [scarlet] kermes, having the stencil perforated and moistened to 
prevent it from sticking. And let this stencil have a pattern of knots, 
which should afterwards be filled in with black millet, and the back- 
ground with white millet. . . 

6 149 [i] v. 

[With drawing^ 

Water-clock which sounds twenty-four hours and the water falls half 
a braccio. 

Water-clock which shows the value [of time]. ^ ^ ^ 




\With drawing of press] 

To press wine and oil in casks bound with iron. 

L 27 r. 

Machines for drying the trenches where the water has overflowed. 


\WithsketcK\ , , . 1 

Four straps for the length and eight across. •, j , 

And each of the straps to be buckled at one end and nailed at the 
other. i-7Pr* 

IMovable bridge] 

[Drawings] . 

Bridge to draw horizontally with a windlass. 

Let be a pulley ^ the windlass. , ’ , c u 

c « will be a pavement of flagstones which has a tube beneath It 

through which the chain passes. 

This is the front of the said bridge. , , , , 

Here is a bridge which carries with it httle wheels, and another, 
better, which travels on small wheels that remain fixed in 

a bi^ the part of the bridge that projects out of the wall; ^ c is the 

part that remains within. ^557. 

f,'hXL which !«.». d,. ..d te hf *= 

-*'°^A11 the transparent part (U netto) has a breadth of a braccio and a 

quarterrand there are si thin boards butithbetter that they should b^ 

The opening two braccia high and the transparent part one braccio 

open below and not above, in order to warm the legs 
^ In the lower part you should use six boards, so tha y 

I7I', ■ ■ 


below than above in order to be able to put the feet to warm; above there 
should be eight, to be able to put the hands which are narrower. 

M 86 r. 


To make a pair of compasses diminish or increase a portion of their 
measurement with equal proportion in each part. 

Bind it spirally with a screw which has as much of it smooth as enters 
in the compasses and all the rest is carved spirally; and this screw may be 
changed at different places throughout the length of the compasses, 
because at different places there are holes equally distant from the 
extremities of these compasses, into which the screw can enter halfway 
as at a quarter as at and one eighth as at and so it proceeds through 
the whole, and it is bound by the nut h of this screw. „ , 

•J rorster i 4 r. 

R O U N D M A C H I N E G I V E N B E L O W 


Make it so that the buckets which are plunging with the mouth 
downwards have such an opening that the air cannot escape; it will also 
be a good thing that the covered exits to the buckets should be of terra- 
cotta so that they may be better able to pass beneath the water; and of 

copper would be best of all. „ 

Forster i 1:0 v. 

[Sketch of loom] 

Threads for weaving ought to be two braccia long. 

Thus one ought to lay the warp. 

Moreover you might set yourself to prove that by equipping such 
a wheel with many balances, every part however small which turned over 
as the result of percussion would suddenly cause another balance to fall, 
and by this the wheel would stand in perpetual movement. But by this you 
would be deceiving yourself; for as there are these twelve pieces and only 
one moves to the percussion, and by this percussion the wheel may make 
such a movement as may be one twentieth part of its circle, if then you 
give it twenty-four balances the weight would be doubled and the propor- 
tion of the percussion of the descending weight diminished by half, and 
by this the half of the movement would be lessened; consequently if the 



first was one twentieth of the circle this second would be one fortieth, 
and it would always go in proportion, continuing to infinity. 

Forster n 89 V, 

Whatever weight shall be fastened to the wheel, which weight may 
be the cause of the movement of this wheel, without any doubt the 
centre of such weight will remain under the centre of its axis. 

And no instrument which turns on its axis that can be constructed 
by human ingenuity will be able to avoid this result. 

0 speculators about perpetual motion, how many vain chimeras have 
you created in the like quest.? Go and take your place with the seekers 



To try again the wheel which continually revolves. 

1 have many weights attached to a wheel at various places: I ask you 
the centre of the whole sum of the weight. 

I take a wheel revolving on its axis, upon which are attached at various 
places weights of equal gravity, and I would wish to know which of these 
weights will remain lower than any of the others and at what stage it will 
stop. I will do as you see above, employing this rule for four sides of the 
circle, and that where you will see greater difference upon the arms of 
the balance, that is that experiment which will throw you the sum of one 
of the gravities more distant from the pole of the balance, that will go 
on and become stationary below; and if you want all the details repeat 
the experiment as many times as there are weights attached to the wheel. 

, . Forster ii 104 v. 

If you wish to make a boat or coracle strong, take . . . (allume splumie) 
and of these make fine cords and weave them together and do as one 
weaves the sacks after making oil of walnut, and of this cover your boat 
as you would with leather. Take from what is in the house, and test this 
by combing as with the sinew of the ox . . . Forster m 35 r 


Take dust of oak-apple and vitriol and reduce it to a fine powder 
and spread this over the paper after the manner of varnish; then write 
on it with a pen dipped in the saliva and it will become as black 
as ink. 




Grash an oak-apple to a fine powder and stand it for eight days in 
white wine, and in the same way dissolve vitriol in water, and let the 
water and the wine settle well and become clear each of itself, and strain 
them well; and when you dilute the white wine with this water it will 

Forster m 39 V. 


To weigh the force that goes to turn the millstone with its corn. 

Forster in 46 v. 


To measure a fall of water. 


For taking away and placing in position rafters for the framework of 
houses and for their roofs. „ , ^ 

Forster in 56 v. 

[Sketch] [Self-closing gate] 

On one side is the shutter. „ ^ „ 

Forster in 58 r. 


Anyone who spends one ducat for the pair may take the instrument, 
and he will not be paying more than half a ducat as a premium to the 

inventor of the instrument and one grosso for the operator; but I have 

no wish to be an under-official. -n ^ 

Forster in 61 V. 


Dry or moist vapour-bath, very small and portable, weighing 
twenty-five pounds, ^ y • 

^ ^uaderni n 9 V. 

[With drawings] 

A method of ascertaining how far water travels in an hour. This is 
done by means of harmonic time, and it could be done by a pulse if the 
time of its beat were uniform; but musical time is more reliable in such 
a case, for by means of it it is possible to calculate the distance that an 
object carried by this water travels in ten or twelve of these beats of time; 
and by this means it is possible to make a general rule for every level 



canal. But not for rivers, for when these are flowing underneath the 

surface they do not seem to be moving above. 

•' ° Leic. 13V. 

\Dr awing: with note ^ lathe for potter 

How many miles an hour with a wind; and here one may see with 

the water of the mill which moves it how many revolutions the wheel 

which is about five braccia makes in an hour; and so you will make the 

true rule away from the sea, making the wheel go one, two, and then 

three times in the hour; and by this means you will regulate it exactly, 

and it will be true and good. r • o 

° Leic. 28 r. 

\Meat-roasting jacJi\ 

Water which is blown through a small hole in a vessel in which it is 
boiled is blown out with fury and is entirely changed into steam, and by 
this means meat is turned to be roasted. „ 

Leic. 28 V. 

[Drawing: wheel on shaft with counterpoise on suspended looped cord\ 

In order to see how many miles a ship can go in an hour have an 
instrument made which moves upon a smooth wheel together with this 
wheel, and so adjust the counterpoise that moves the wheel as to cause it 
to move for an hour; and you will be able to see how many revolutions 
this wheel makes in the hour. The revolution of the wheel may be five 
braccia, and it will make six hundred revolutions in a mile. And the 
glass should be varnished or soaped on the inside, so that the dust that 
falls from the hopper may attach itself to it; and the spot where it strikes 
will remain marked; and by this means you will see and be able with 
certainty [to discern] the exact height where the dust struck, because it 
will remain sticking there. t • 

o Leic. 30 r. 

; Warfare 

‘When besieged by ambitious tyrants I find a 
means of offence and defence in order to 
;; preserve the chief gift of nature, which is 

I liberty.’ 

I ^ can noiselessly construct to any prescribed 

I point subterranean passages either straight or 

? winding, passing if necessary underneath trenches 

I or a river.’ 

\How to make a pontoon\ 

Since every river current is swifter in the centre of its breadth than 
at its sides, and flows faster on its surface than in its bed when the course 
is equal, and a movable bridge made upon barges is in itself weaker in the 
middle of its length than towards the extremities, therefore I conclude 
that as the greater weakness of the bridge is accompanied by the greater 
percussion of the water this bridge will break in the centre. 

Make it so that in the movement of the bridge the length of the 
barges will always find itself in line with the current, when the 
movement will be so much easier as the barges receive less percussion 
from the water. 

C.A. 176 r. c.', 


The tower must needs be massive as far as the end of the scarp, then 
in order that powder may not be thrown there you must make the 
windows high. 

A W A Y T o M A K E A C U I R A s s 

If you place between two thicknesses of cloth scales ofiron[?]^ and 
with this make a doublet you may take it as certain that no point will 
ever be able to penetrate. 

c,A. 358 V. a 

Again a bombard that takes a projectile weighing a hundred pounds 
is of considerably more use in the field than a small cannon, for that with 
pieces of rock inflicts considerable damage upon the enemy, and the 
small cannon or rather its ball, being of lead, does not rebound after the 
first blow by reason of its weight, and on this account it is less useful. 

If you set an arrow so that it is just in equilibrium on top of a stone 
which seems on the point of falling over, you will perceive that a large 
bombard if discharged at a distance of ten miles from this arrow will 
cause such a tremor of the ground as to make the said arrow fall, or the 
stone upon which it is balanced. 

Again if you discharge a small bombard in a courtyard surrounded 
by a convenient wall, any vessel that is there or any windows covered 
with cloth or linen will all be instantly broken; and even the roofs will 
^ MS./. {ferro?) 



be somewhat heaved up and start away from their supports, the walls 
and ground will shake as though there was a great earthquake, and the 
webs of the spiders will all fall down, and the small animals will perish, 
and every body which is near and which is possessed of air will suffer 
instant damage and some measure of loss. 

But this small bombard should be discharged without its shell or if 
you so desire after the fashion of the curtail and it will cause women to 
miscarry and also every animal that is with young, and the chicks will 
perish in their shells. , , 

C.A. 363 V. d 

Having to make mounds of earth on the two opposite sides of the 
river this is the most expeditious manner in which it can be done, 
provided you have men with hand-barrows: 

Allowing six shovelfuls to each hand-barrow, and casting the earth 
at a great distance: 

The diggers d enter underneath a shovelful, always drawing them- 
selves back, and the diggers h make another second shovelful below, that 
is deeper down, always going forward; and if there were two other similar 
lines of diggers these would go beneath the third and fourth shovelful, 
and so successively they would be able to continue from hand to hand. 

Here many men become fatigued merely by taking loads for so great 
a distance, so that we have to consider whether it is better that the men 
should remain in one spot and throw the soil from one to another, or 
should all be employed in digging and throwing, or whether some 
should be carriers of this soil and others throwers. For as regards the 
place where this earth is discharged it requires as much effort for 
the shovelful of the first or of the second to reach it in one way as in the 
other: nothing therefore need be considered here except the convenience 
and endurance of the workers. 

C.A. 370 r. b 

[With sketch of cannon\ 

The mouth one eighth of its diameter thick, and at its union with the 
tail one q uarter of its diameter thick. v 

^ Tr. 61 a 

If you are attacked by night in your quarters or if you fear to be, 
take care to have mangonels in readiness which can throw iron caltrops; 

^ MS. cortaldo, ‘Curtail, a kind of cannon with a comparatively short barrel, in use in 
the sixteenth and seventeenth centuries.’ Oxford English Dictionary. 

- 180 ' . 


and, if you should be attacked, hurl them in among the enemy and you 
will gain time to set your men in order against their assailants, the 
outwitted enemies, who because of the pain caused by the wounds iii their 
feet, will be able to effect little. And the plan of your attack you will 
make thus: — divide your men into two squadrons and so encircle the 
enemy; but see to it that you have soles to your shoes and that the horses 
are shod with iron, as I have said before, since the caltrops will make no 
distinction between your men and those of the enemy, and see that each 
mangonel throws a cartload of the said caltrops. 


If you wear between the foot and the sole of the shoe a sole of cloth 
woven of cords of cotton of the thickness of a finger you will be safe 
from caltrops, which will not thrust themselves into your feet. 

If you wish to be safe from light shifting sand upon the galleys, have 
heavy river sand strewn upon the gangway and where you have to set 
your feet; and pitch will fix this, and keep sacks always in readiness for 
when they may be needed. gg ^ 

You should make caltrops of plaster with the arch of iron and the 
moulds in three parts, and then the points should be filed. \Below •— sketches 
of three caltrops with four points and of one with eighty each of the 
four Being duplicated close together — below this is written ^double caltrop\\ 

These caltrops should be kept in a leather bag by the side of each 
person, so that if the expected victory should be changed to a defeat 
through the strength of the enemy, the fact of these being scattered 
behind them would be the cause of checking the speed of the horses and 
of bringing about the unhoped-for victory. 

But lest in retreating this crop should be the cause of a similar mistake 
for yourselves, you should first have made ready the irons for the horses 
in the form represented below, and have nailed between the iron and the 
horse’s foot a plate of steel as thick and wide as the above-mentioned 
horse’s iron. 

And in the case of foot-soldiers they should have iron plates fastened 
to the soles of their shoes, not tied tightly, so that they may be able 
easily to raise their heels and take steps and run when necessary 
without any restraining obstacle, and the knot that is left loose 
should be as it is represented here below. 

■ ^ m • 


Moreover if you have a small bag of them by the side of each naval 
combatant and they are then thrown by hand on the enemy’s galleys or 
ships they will be sowing the seed of the approaching victory; but you 
should have the shoes bound with iron, as was said above, and covered 
over below with tiny points, in order that if it should come about that 
soft soap be thrown upon your ship you will be able to keep your feet, 
even though the enemy should throw chalk in the form of powder in 
such a dense cloud as to devastate the air which is breathed into the 

You should set up four stations at four positions in the length of the 
ship, and at each of the four stations let there be a small barrel with a 
certain quantity of water, and large syringes which serve to force the 
water out through many small holes, so that the water may become 
changed into spray and may thus accompany the dust of the chalk and 
draw it downwards. 

\Three sketches — below^ 

syringe; iron sole for shoes; iron for horse for caltrops. 

Tr. 90 a 

[Drawing of fire-balF^ 

This ball as it is thrown becomes extinguished, and as it reaches the 
ground the canes which are bound at the top with linen cloth that has 
been set alight are driven into it, thus igniting the powder which is all 
round a piece of tow that has been soaked in turpentine, the rest of it 
being wrapped in hemp which also has been soaked in turpentine, oil of 
flax, and pitch, and the wrappings should be thin in order that the flames 
may get the air, for otherwise you will do nothing. b 4 r ^ 


This rhomphea can be drawn with army horses, as the ancients drew 
other instruments. 

This [small drawing of instrument^ is attached to the centre of a piece 
of plank, or piece of chain, or stout cord, that is fastened to a lump of 
stone heavier than the plank and so drawn behind the plank, which on 
the front edge is full of spontoons of the length of a cubit, and the said 
plank will be twelve braccia long, and its surface is studded with nails. 

' ■ B 7 'I. ■ 

^ The notes on instruments of warfare in this manuscript, B of the Institut, are 
extensively derived from the De re militari of Roberto Valturio. 



A scorpion is a machine which can hurl stones, darts and arrows; and 
if it is made large it will be suitable for breaking the machines of the 

Other authors are of opinion that a scorpion is a poisoned arrow 
which however little it may touch the blood causes instant death. And 
it is said that this weapon was found among the Scythians, others say 
among the inhabitants of Candia. The brew was made of human blood 
and serpent’s venom. This weapon should not be used except against 
traitors, for it comes from them. b 7 v. 


The catapult according to Nonius and Pliny is an instrument 
invented by that Ticlete% which threw a dart of three cubits, and with 
iron on three sides, thrown by means of wood released from the con- 
, traction of twisted sinews. 

A bit of thin steel also springing back when released will have power 
to drive a dart swiftly when it stands in its course. b 8 r. 

I'j REOMPff£J 

( The rhomphea is an instrument which throws out long brands of 
burning wood; it was used among the Thracians according to Aulus 
r Gellius, and by the men of other nations it was called fiammea. 

T H E B o w 

The bow is said to have been invented by the inhabitants of Arcadia, 
some say by Apollo; those of Candia call it Scythian as coming from 
Scythia. And it is much in use among the eastern peoples. They make 
arrows of canes for these bows, and in their battles there are sometimes so 
many of them in the air that the day becomes so darkened as to seem 
like night. So for this reason they have a hatred of the clouds and the 
rain and the winds no less, because they divert the course of their arrows; 
and these causes often bring treaties and peace among them. b 8 v. 

The spikes {murid) or caltrops {triboli) are for use on the field of 
battle, in order to scatter them on the side on which there is reason to 
expect the assault of the enemy, and also for throwing among the 
enemy when they follow up their victory. 

^ Tiglath Pileser? (Ravaisson-MoUien). 



The scalpro was a sharpened iron used to prick and control elephants. 
Livy in the Seventh Book of the Carthaginian War says that many more 
elephants were killed by their own governors than by the enemy. For 
when these beasts got enraged with them the governor with a mighty 
blow thrust the sharp scalpro between the ears where the neck joins the 
spinal column; and this was the most rapid death that could be given to 
so huge a beast. 

The veruina according to what I find in a comedy of Plautus^ is a 
long spear with a sharp iron point for hurling. 

The soliferreo is a kind of weapon entirely of iron which the soldiers 
used to throw at their first assault. Livy mentions it in the fourth 
book of the Macedonian War. 

Fonda (sling) is made of a double cord and is somewhat wide where 
it is bent, and being weighted with a stone and then turned twice in 
rapid succession by the arm it releases one of the cords, and the stone 
flies with a noise through the air as if it proceeded from a catapult. 
Flavius® says that it is found among the inhabitants of the Balearic Isles, 
that they have supreme skill in the use of it, and that the mothers do not 
allow their children any other kind of food than what has been brought 
down by them as a mark with a stone shot from a sling. Pliny on the 
other hand says that this sling was invented by the Syro-phoenician 

Glande are leaden balls shot with catapults and slings. ^ ^ ^ 

Auctori according to Celidonius are sickle-shaped weapons with a 
cutting edge bn one side only and the length of a braccio. They have 
the handle forked after the fashion of the tail of a swallow. They are 
not carried in a sheath but bare, attached to the girdle. 

Danish are a rather long kind of hatchet: they are said to have been 
much in use among the Danish peoples. But what has to be taken into 
account with respect to instruments of warfare made of iron is that that 
which has been steeped in oil will have a fine edge, and that which has 
been immersed in water will be rough and brittle. Those which are 
soaked in the blood of a goat will be the hardest. Oil, white lead and 
pitch preserve iron from all rust. 

^ The reference is to Plautus’s Bacchides^ Act 4, Scene 8, 1 . 46. 

Si tibi est machaera, et nobis veruina est domi. 

* Flavius Josephus? (Ravaisson-Mollien). 




I fake (scythe) is of iron, crescent-shaped, and with a staff fastened 

i to one of its horns. This weapon was much in use among the Thracians 

and in naval combats no less than on land. It was afterwards converted 
; for the use of husbandmen and peasants. 

They were used by the Romans upon their ships; unheard of in 
size and skilfully manipulated by means of ropes they severed the ropes 
of the lateen yards as though they were razors, and caused the sails to 
‘ fall at the same time as the yards, so that what ought to have been a 

help to the enemy was a great hindrance to them. 

I Fragilk/ia is a ball half a foot across, filled with small barrels made 

I of paper and crammed with pepper, sulphur and ... of Corsica 

J {conocorsko). And whoever receives the smell of it falls in a swoon; 

r and in the centre of this ball is the powder of a bombard which when 

kindled sets fire to all the barrels, and when it is first thrown among the 
troops with a sling the fire catches a wisp of straw, and the sparks proceed 
to spread over a space of a hundred braccia. ^ ^ 

C A R W I T H S c Y T H E s 


These cars armed with scythes were of various kinds and often did 
no less injury to friends than they did to enemies, for the captains of the 
armies thinking by the use of these to throw confusion into the ranks of 
the enemy created fear and loss among their own men. Against these 
cars one should employ bowmen, slingers and hurlers of spears, and throw 
all manner of darts, spears, stones and bombs, with beating of drums and 
shouting; and those who are acting thus should be dispersed in order 
that the scythes do not harm them. And by this means you will spread 
panic among the horses and they will charge at their own side in frenzy, 
despite the efforts of their drivers, and so cause great obstruction and 
loss to their own troops. As a protection against these the Romans were 
accustomed to scatter iron caltrops, which brought the horses to a 
standstill and caused them to fall down on the ground from pain, leaving 
the cars without power of movement. ^ 


You ought when you wish to make the passage of a river with an 
army to make use of wine-skins attached to the saddle, and, as the horses 
are not able to swim much on account of the waves leaping up, you should 



carry an oar fastened to the neck behind so that [the rider] can work it J 

when necessary. biov t 

\With drawings: Jiammeay pilocrotho, arzilla, crusida, lampadcy astulal 

The fiammea is a ball put together in this manner: Let the following 
things be boiled together, the ashes of willow, saltpetre, aqua vitae, 
sulphur, incense, and melted pitch with camphor, and a skein of Ethiopian 
wool which after merely being soaked in this mixture is twisted into 
the shape of a ball and filled with sharp spikes and thrown on ships with 
a cord by means of a sling. 

This is called Greek fire, and it is a marvellous thing and sets fire to 
everything under the water. Callimachus the architect was the first 
to impart it to the Romans, by whom it was afterwards much employed 
and especially by the Emperor Leo, when the eastern peoples came 
against Constantinople with an infinite number of ships which were all 
set on fire by this substance. 

Pilocrothoy arzilla, crusiday fiammeay lampadcy although they differ 
are nevertheless almost of the same substance, and their fire is similar to 
that spoken of above, that is of the fiammea except for the addition to the 
said composition of liquid varnish, oil of petroleum, turpentine and 
strong vinegar, and these things are first all squeezed together and then 
left in the sun to dry, and afterwards twisted about a hempen rope and 
so reduced to a round shape. Afterwards it is drawn with a cord, and 
some bury the point of a dart in it, transfixing it after having wetted the 
dart, some bury very sharp nails within it; and a hole is left in the said 
ball or mass for the purpose of setting it on fire and all the rest of it is 
smeared with resin and sulphur. Our forefathers made use of this 
compound pressed tightly together and bound to the end of a spear, 
in order to ward off and resist the impetuous fury of the enemy ships. 

Lucan says that Caesar used to make this fire in order to throw it by 
means of lamps upon the ships of the Cerusci, a people of Germany; he 
burnt not merely the said ships, but the buildings constructed upon the 

borders of the sea were consumed by a similar fire. 

•' B 30 V. 

Tht folgorea is a mortar with an opening in its tail circular in 
form, in the centre of which occurs a thin chanicula [chamber?] of iron 
finely perforated, with the hollow of it filled with fine powder; and it is 
made thus for two reasons, first, that when it reaches the centre of this 
■ ■ 186 



ball; the fire, which passes through the chamber, lights in an instant all the 
rest of the powder that finds itself pressed within this ball, secondly, so 
that the hole of the mortar may not become worn. And this round 
opening will not resist the might of the powder unless it is made of fine 
copper, but the rest may be made with four parts tin to every hundred of 
copper, and this is the best machine that it is possible to make. ^ ^ 

The clotonbrot is a ball thrown by a trabiculo, that is a lesser mangonel 
which is a braccio high and filled with the ends of cartridges packed 
all together in a tiny space. It is used for throwing into a bastion and 
there is no remedy that avails against its pestilential effect, but for this 
purpose its use would be a mistake because it does damage to you as 
well as to the enemy. And if you throw six or eight of these balls 
among the enemy you will certainly be the victor, so it is good to 
throw it in the midst of them, and light the fuse within which will 
at last set fire to the centre of all the sticks. 

This is for ships. 

When the ships are engaged, have fuses to keep the enemy back, 
and at that moment throw balls full of lighted fuses among the enemy, 
that is to say upon the ships, and the enemy being occupied in protecting 
themselves from the fire will abandon their defences. 

B 31 V. 

\With drawing of two cannon placed vertically with stand between them\ 

Whoever wishes to make trial which is the better must raise them 
on end and two judges should be in the centre, and after first firing the 
one it must be noted how much time there is from the explosion to the 
return of the ball to the ground and then the same is done with the other 
and the one which takes longer will have the honour. 

But see that the tubes are of equal length, that the touch-holes 
work freely, that the balls are of the same weight, and the powder is 
from the same keg. ^ ^2 r 

[With drawingl 

If you wish to be able to ford a river with your army when you 
please you will proceed as follows: — make a boat of osiers of willow and 
make it with the brims double in such a way that they open from below, 
and fill the body of it with gravel. And when you are at the place that 
you wish, open the store of gravel from below so as to cause it to fall to 

■ 187 ■ 


the bottom; after doing this close the receptacle and return to the bank 
to reload. You will need to have a number of these machines, but the 
actual body of the boat should be bound outside with oxhide to prevent 
it falling to the bottom. 

[With drawing 

To make an airgun which shoots with marvellous force you should 
proceed as follows: — stretch a steel wire the width of a finger on a wire- 
drawing machine by means of a windlass; then temper it, and beat 
round about it two plates of fine copper which you stretch on the wire- 
drawing machine. Then half to half solder them together with silver, 
wind thick copper wire about it and then smooth it with a hammer, but 
first solder it. And do this three or four times in the same way. And 
make [the airgun] two braccia long and make it so that it can shoot a 
dart of a third of a braccio which is of steel. 

B 32 V. 

The architronito is a machine of fine copper, an invention of Archi- 
medes, and it throws iron balls with a great noise and fury. It is used in 
this manner: ~ the third part of the instrument stands within a great 
quantity of burning coals and when it has been throughly heated by 
these it tightens the screw d which is above the cistern of water a b c\ and 
as the screw above becomes tightened it will cause that below to become 
loosened. And when consequently the water has fallen out it will descend 
into the heated part of the machine, and there it will instantly become 
changed into so much steam that it will seem marvellous, and especially 
when one sees its fury and hears its roar. This machine has driven a ball 
weighing one talent six stadia. 

° ° B 33 r. 

\Ftre-baH\\Wtth drawing 

This ball should be made of melted pitch, sulphur and tow of hemp 
rubbed together so that when it burns the enemy may not carry off the 

This ball should be two and a half braccia in height and filled with 
tubes which can throw a pound of balls, and these should be coated with 
pitch within the tubes so that they do not fall. 

The tubes should be a braccio in length, and made of pasteboard 
after the manner of spokes, and the space between them should be filled 

188 ■ 


with plaster and wadding; and the ball should be thrown upon the 
bastions by means of a mangonel. 

The centre of it will be a cannon-ball to which the tubes serve as 
good epaulets, or a hollow ball of bronze which may be partly filled with 
powder, with its circumference perforated so that the fire is able to 
penetrate to the tubes; and the ball should be all tied up on the outside 
except for a hole to serve as a passage for the fire. ^ ^ 

\With drawings] 

Cortalds (short pieces of artillery) are good against big ships. 

The serpentine [passavolante) is useful for light galleys in order to 
be able to attack the enemy at a distance. It can throw four pounds of 
lead and ought to be as long as forty cannon balls. 

This spontoon will fasten the instrument into the ship if the blow is 

This zepata is good for setting fire to ships which have kept a 
blockade after having besieged some harbour or other ships in the har- 
bour, and it should be made thus: first wood a braccio above the water, 
then tow, then powder as used for a bombard, then tiny faggots and so 
gradually larger ones; and put iron wires and burning rags on the top; 
and when you have the wind as you want it direct the rudder. And as 
the fire m spreads in the ship the bent wires will set fire to the powder, 
and it will do what is necessary. 

It is also useful for setting fire to bridges at night, but make its sail 


Acinace. Acinace is the name of this knife: it was so called among the 
Scythians and Medes, according to the statement of Aero. 

Daga. This among the Ligurians was called daga. 

Ensis. Gladius. Ensis and gladius are a kind of weapon, and, accord- 
ing to Quintilian in the tenth book of his Institutions, they are the same 

According to Pliny in the sixth book of Natural History, the gladius 
was invented by the Lacedaemonians. 

According to Varro, when the gaesum (javelin) became obsolete 
the gladius was used in its place. It has been called acUs because it was 
used for the destruction and death of the enemy. 

189 ‘ 


Spada^ enstsy and gladius are names of arms universally known and 
especially among the ancients. 

Arpa, ArpUy according to Lucan in the ninth [book], is said to be a 
sword of the shape of a sickle with which Perseus slew the Gorgon. 

The bows were called 

B 41 r. 

Lingula, according to what Naevius says in one of his tragedies called 
Ceisonia, was the name of a small knife of the shape of a bird’s tongue. 

Machaera is a kind of long weapon with one part of it sharpened. 
Caesar mentions it in the second of his Commentaries. 

Stragula is a kind of lance for throwing and for using with the hand. 
Caesar mentions this also in the second of his Commentaries. 

Doloni are a kind of weapon mentioned by Plutarch in the life of 

Others are of the opinion that doloni are whips with daggers con- 
cealed in their handles. 

Sica is a small knife used by assassins in ancient times, who were 
called sicarii from the name of the knife according to Quintilian in the 
ninth book of the Institutions. 1 

341 V. 

PugiOy according to Pompeius Festus, is a short double-pointed knife. 

Varro says thsitpugio is the name given to a long lance with iron. 

Clunade {clunaculum) is a sacrificial knife. 

Secespita is a long knife with a round handle made of a piece of ivory 
and ornamented with gold and silver. It is used by the high priests and 
the flamens for the sacrifices. 

Some say it is the axe (scurd) and some that its edge resembles that 
of the manara. 

Macro is identical with ensis and gladius, according to Priscian in the 
second book of the Ars Grammatica. 

AcUdeSy according to the opinion of Servius, are a kind of weapon so 
ancient as to have been entirely overlooked in war. Nevertheless we 
read that they were pieces of wood, some half a cubit in length and some 
circular; and in them were fixed iron points which were sharp and pro- 
jected; and they were hurled among the enemy with a cord or leathern 
thongs, and he who received the blow soon knew who had given it. 

3 4.2 T. 

^ cf. ‘per abusionem sicarios etiam omnes vocamus, qui caedem telo quocumque 
commiserint.’ Quint. 10, i, 12. 


Telo (teluin) was the word generally applied by the ancients to all 
those things which in war were suitable to be thrown with the hands, 
such as darts, clubs, arrows, spears, lances, stakes and stones. 

Veruto. The mruto (verutum) (javelin), according to Nonius Mar- 
cellus, is a small weapon and very straight. 

Fusti. Fusti [fustis) (club) were the first weapons that the human race 
used, and they are today called stakes by countryfolk; and their points 
were somewhat charred. 

Baculo. The baculo {baculum) is a stick without a hook to it with 
which unhappy slaves were beaten. 

Haste {hast a) (spear) is said to have been invented by the Lacedae- 
monians. They are excellent and . . .? {plestante) when made of ash or 
hazel, but better still when made from the service tree, because this is 
more supple and flexible. 

Astili are the smaller lances which are thrown deftly with the hands. 

Cuncti {conti) are very long and stout pikes without iron but having 
their point sharpened. Lucan makes mention of them. 

Lancea. Pliny says of the lance that it was invented by the Aetolians. 
Varro says that lancta is a Spanish word. ^ ^ 

Filo {pilum) was a spear in use among the Romans, resembling the 
gaesum of the Gauls and the sartssa of the Macedonians. And these 
spears were divided in their length in two equal parts and the heads were 
placed at each end. They were joined together with fish glue and at 
every half cubit bound with gut. Writers say that these spears were 
so perfect that if they were suspended by a cord in the form of a balance 
they did not bend. And if one first draws it back and then drives it 
forward with fury there is no armour of sufficient strength to resist it. 
They were much in use among the Bretons. 

Gtese {gaesum) is a weapon used by the people of Gaul, and they are 
no less useful for hurling than for use in any other way. 

Ruma^ pilum^ rumex and telum resemble each other and resemble 
also the sparus of the Gauls. 

Jaculo (javelin) is said to have been invented by ffEtolus the son of 
Mars, and to this Hermes, Varro, Pompeius Festus bear witness, affirm- 
ing that javelins are rude and fashioned by rustics of poor mean con- 
dition but suitable for scattering on all sides. 


B43 r. 


Sarissa. Sarissa, according to Pompeius [Festus], is a Macedonian 

Gabina. Gabina is the name given by the Illyrians to a certain kind 
of weapon of the shape of a hunting-spear (venabulum) ox pike. 

Securis (battle-axe) is called also semicuris or semiqutris, 

Tragula, Tragula is a spear with a very sharp point of the shape of a 
javelin or dart which can be thrown by the hand according to Varro, 
Pompeius, and Caesar in the fifth of the Commentaries. 

Clava. Clava [club] is a kind of weapon which was used by Hercules, 
and it was so called because it was a big strong stick studded with sharp 
nails, and this in these rude times would be considered a very magnificent 

Cathegia, [Boomerang?] Some bdieve this clava to have been the 
cathegia which Horace calls caia and that the cathegia was a kind of dart 
in use among the Gauls which comes back at the wish of the thrower. 
According to Virgil it was greatly in use among the Germans; the 
knights made a great use of it against the infantry. b 43 v. 

Dolabra, that is, double-cutting. 

It is called two lips (Jabbri) after what Livy states in the eleventh 
book^ of the Punic War, where he relates that Hannibal sent five hun- 
dred Africans armed with these in order to lay waste to their foundations 
the walls of a town. 

Bipenna, This weapon is so called because it has a sharp edge on 
both sides. The term is usually applied to it by Quintilian, in the first 
book of the Institutions. B44r. 

The cross was invented among the Germans, and this weapon is said 
to be in the front rank of deadly weapons, seeing that if it is thrown 
either with a cord or without among the ranks of the enemy it never 
falls there in vain. And this because it runs edgewise through the air 
and if it does not catch the enemy with one of its points it catches him 
with two, or not finding the enemy there it is driven into the ground, 
where it inflicts no less damage upon the enemy than if it struck the 
horses and the footsoldiers. From four to six of these are carried round 
the belt when one goes into the combat. 

^ As M. Ravaisson-Mollien has stated, the passage referred to is in Book XXI, para, xi, 
but as however Books XI to XX have been lost, Book XXI follows Book X. . turn 
Hannibal occasionem ratus, quingentos ferme Afros cum dolabris ad subruendum ab imo 
murum mittit.’ 


^Drawing of caltrops with cord and thongl 

This method was much in use among the Jews and the neighbouring 
peoples of Syria. And they throw them with cords and long thongs 
among the enemy on finding themselves vanquished and routed by 
them; whereby they being thrown down are made to cease their course. 

And they also sow them upon their own line. 

Telico, These were in use among the first men; and they were made 
of cane, that is to say that having taken a piece of cane with two knots 
they split one through the middle and used it as the feather of the arrow; 
and the other they made into a point and filled it with earth so as to 
weight it, and they threw these by means of a cord. b 44 v 

Scourge (fagellum). This also was among the number of the primi- 
tive and rustic arms. 

Scythian arrow. The arrow is a simple weapon which was much in 
use among the Arabs. It was invented by the Scythians, and consists of 
a piece of green wood of which the end has been burnt; and it may be 
thrown either by means of a cord or without. If it is held it may be used 
also as a javelin. 

Ganci, ruffili and roncili are maritime weapons in use among pirates. 
By means of hooks they are accustomed to grapple the edges of ships, 
and if any of the ship’s defenders should approach them they wound 
them and drive them before them, and then return to the edges where 
they were before and dig them deep into the ships so that they cannot 
escape- ^ B45r. 

Sirile is a very long spear; it was found among the Numidians. They 
often used it in order to throw down their enemies, and they rode on 
horseback without saddle or stirrup, armed only with a doublet stuffed 
with cotton over which were fastened the hooks of the long sirile; and 
[the enemy] taken by surprise were easily thrown down. 

Cariffe is a broad spear with which one can attack from afar. And if 
it should come about that the combustible ball should be captured, the 
soldier can start it by striking it with the sharp iron point that is at the 
head of the spear, and thus recovering it woid scourge the wretched 
soldiers [of the enemy]. 

Mtricide is a spear three braccia in length, and five braccia and a 

z 193 


half when extended: the soldiers use it in the way in which rustics thresh 

Malcoliy according to Ammianus Marcellinus, are a kind of dart or 
arrow. The stem is of cane and where the cane ends a distaff is joined like 
that used for spinning, and on this distaff the iron is fixed. Tow steeped 
in pitch should be placed in the hollow of the said distaff, and it should 
be set fire to and thrown gently so that the rush of the air may not ex- 
tinguish it. Some say that within this cavity there should be an in- 
exhaustible store which should consist of resin, sulphur, and saltpetre 
which should have been liquified with oil of laurel, or some say petroleum 
oih and fat of duck, and marrow of meat, and fennel, and sulphur, resin 
and camphor with . . . [rasa?] and tow. This mixture among the ancients 
was called combustible, that is something suitable to burn, also tow, fat, 
and petroleum. ^ ^ 

The Manara was much in use among the Romans. 

Irish and English bows. But the Irish in place of one corner of the 
bow have a piece of sharpened iron of the length of a cubit. 

The English and the Irish are almost the same length, that is four 
braccia each. 

Syrian bow, made of horns of buffalo. 

German bow, made of two pieces of steel and how they are set. 

The dart of the cross-bow works in this manner: namely, when the 
arrow issues forth from the cord and passes over the roller, the ring at the 
extremity of the arrow causes it to leap back after it has struck; but 
the iron continues and performs its function. 

The dart of the bow by which the arrow remains attached to the 
cord is an awl a quarter of a braccio in length, all of iron finely tempered; 
the feathers of the tail come away from the arrow as it flies on its way. 
Some there are which make a prick resembling that of a needle full of 

B 46 r. 

[Drawing — soldier on horseback galloping 

This is a mounted carabineer which is an extremely useful invention. 
The said carabineers should be provided with pouches full of rolls of 
plain paper filled with powder, so that by frequently inserting them they 
subdue the excessive numbers of the enemy. And these carabineers 
should stand in squadrons as do cross-bowmen, so that when one part 
^ MS. olio petr olio. 



fires the other loads; but first make sure that you have accustomed the 
horses to such noises; or else stop up their ears. 

Order of mounted cross-bowmen on the open field: m n are cross- 
bowmen who as they turn left draw back loading, r t are those who go 
forward with cross-bows loaded, and these four files are for one route; 
a b are four files of cross-bowmen who turn with bows unloaded in order 
to load them anew; c d are those who come upon the enemy with their 
bows loaded; and this arrangement of eight lines is employed in open 

And have it so that those who have unloaded come through the 
centre, so that if sometimes they have been routed by the enemy the 
cross-bowmen who are loaded, holding themselves on the flanks, may 
cause greater fear to these same enemies. 

Order of mounted carabineers: 

See that they are well supplied with guns with a thin single fold of 
paper filled with powder with the ball within, so that they have only to 
put it in and set alight. Being thus ready they will have no need to turn 
as have the cross-bowmen when they are preparing to load. ^ ^ 

If anyone had formed the design of capturing a tower situated on 
the sea, he would cause one of his followers to take service with the com- 
mander, and when the guard was withdrawn he would affix to the battle- 
ments the rope-ladder given him by the enemy and would fill the walls with 
soldiers. In order to prevent this, you should divide the tower into eight 
sets of staircases, spiral in shape, and divide into eight parts the ramparts 
and the soldiers’ dwellings below; then, if one of the mercenaries should 
be disposed to be a traitor, the others cannot hold communications with 
him, and the section of the rampart will be so small that there will not 
be able to be more than four there. The commander, whose quarters are 
above those of all the others, can drive them out by attacking them from 
the machicolations, or shut them up by means of the portcullis and then 
put smoke at the entrance to the spiral staircases. On no account is it 
necessary that any alien soldier should lodge with the commander, but 
only his own family. 

The confederate of the scaler of the wall should carry with him a ball 
of strong thread when he takes service with the commander, and when 
the opportunity comes the guard will draw up with this thread a coil of 


\With drumin^ 

How one ought to defend oneself against a furious attack by 
soldiers who are attacking a hill fort. Namely by taking barrels and 
filling them with earth and rolling them down the slope upon the enemy, 
for these will be of great benefit to those who have despatched them, 

B 56 r. 

\JVith drcmings] 

This shield should be made ot tig-wood inside, with cotton of the 
thickness of a quarter of a braccio outside it, and outside the cotton it will 
be well to put fustian with a coat of varnish; or if you make the outside of 
cotton and the inside of isinglass and tragacanth and varnished, with 
half the amount of cotton, plain and compressed, with nails going from one 
surface to another, it will be satisfactory, and you can dry it in a press. 

These balls should be filled with small dust of sulphur which will 
cause people to become stupefied. 

This is the most deadly machine that exists: when the ball in the 
centre drops it sets fire to the edges of the other balls, and the ball in 
the centre bursts and scatters the others which catch fire in such time as 
is needed to say an Ave Maria, and there is a shell outside which covers 

The rockets of these balls should be made of paper, and the space 
between each filled with plaster ready to be moulded, mingled with the 
clippings of cloths. And they should be set alight with a pair of bellows 
which will cause the flame to extend to the centre of the ball among the 
powder, which separates at a considerable interval from each other all 
the balls filled with rockets. 

Wheel full of tubes of carbines for foot-soldiers. ^ ^ 

B 59 r. 

\With drawings^ 

If you have not any information from within as to who will draw up 
the rope-ladders, you will ascend first by placing these irons in the 
crevices a braccio’s space apart in the manner shown above. 

And when you are at the top, fix the rope-ladder where you see here 
the iron m\ let it be bound with tow so that you do not make any sound 
and there remain. Then if it should seem that you ought to draw up other 
ladders, do so; if not, cause the assailants to ascend quickly. The hook 
which is attached to a brace of ropes has above it a ring to which is fixed 


Royal Library, Windsor 


a rope, and this is drawn up by a jack to the iron above, and to this you 
attach a second time the hook of the above-mentioned braces. 

These ladders are made to carry two men. They are also useful for 
a tower where you are afraid lest the rope-ladder may be detached by the 
enemy; they should be driven so far into the wall that three eighths [of a 
braccio] is buried and one eighth is free. These pyramidal irons should be 
half a braccio in length and their distance apart half a braccio. ^ ^ 

\With drawings^ 


It is also necessary to reflect how one ought at one’s convenience to 
make the passage of rivers. First set a man upon two bags bound 
together, then if you find the bottom to be suitable and that the river is 
dangerous through the rapidity of its course make use of the method 
represented below. 

If the river is dangerous by reason of its current you should set two 
lines of horses across the river at a distance of six braccia one from the 
other, and the horses in the lines should be so near as almost to touch each 
other, and the line or company of horses should have their heads turned 
towards the current of the water, and this is done solely in order to 
check and break the fury and impetus of the water. And between the 
one company and the other pass the soldiers both those with and those 
without arms. The company that is higher up the stream should be 
made up of the bigger horses in order to be better able to stem the rush 
of the river, that lower down serves to hold up the soldiers when they 
fall, and to act as a support for them as they make the passage. ^ ^ 

\With drawing^ 

Make shelters by interlocking shields to withstand the fury of masses 
of arrows. 

The method in which the Germans when in close order link together 
and interweave their long lances against the enemy, stooping down and 
putting one of the ends on the ground and holding the other part in their 

[With drawings] 

If the water is so high that infantry and cavalry cannot pass, the river 
should be diminished by leading off many streams, as Cyrus, King of the 



Persians, did at the taking of Babylon upon the river Ganges [r/V] which 
at its maximum breadth is ten thousand braccia, Alexander likewise upon 
the same river, Caesar upon the river Sicoris. 

If it should come to pass that the river was so deep that one could not 
cross it by fording, the captain ought to make a sufficient number of 
streams to carry off the water and afterwards give it back below to the 
river, and in this way the river would come to be lowered and could be 
crossed with ease. Alexander employed this method in India against 
King Porus at the passage of the river Hydaspes, and Caesar did the 
same in Gaul (and also in Spain) upon the river Loire; having arranged 
his cavalry in two companies he caused the soldiers to pass through the 
middle of them. Hannibal did the same on the Po with elephants. 

B 6i r. 

[With drawings\ 

The Egyptians, the Ethiopians and the Arabs in crossing the Nile are 
accustomed to fasten bags or wine-skins to the sides of the forequarters 
of the camels in the manner shown below. 

In these four rings in the net the baggage-camels put their feet. 

The Assyrians and the inhabitants of Euboea accustom their horses 
to carry sacks in order to be able at will to fill them with air. They carry 
them instead of saddle-bows above and at the side and well covered with 
plates of dressed leather, so that a quantity of arrows will not penetrate 
them, since they are no less concerned about a safe means of escape than 
the hazard of victory. Thus equipped a horse enables four or five men 
to cross at need. ^ 

B 01 V. 

[How infantry cross rwers\ 

If it should come to pass that infantry have to pass a river which is 
dangerous by reason of the force of its current, this is a sure way: — let 
the soldiers join arms one with another and form themselves into a line 
after the manner of a stockade, linked together by their arms; and let 
these files advance along the line of the water and let no one go across 
its course, and this is a sure way because the first being above the water 
is the one who sustains its first onset, and if he was alone the water would 
throw him down, but all the others below him hold him up and use him 
as their shield; and so by this means one after another they cross in safety. 
So it is with all: and if the fall of the river is from right to left each man 
in the file as he proceeds from the first to the second bank ruffles the 



course of the stream with his right shoulder, and .on his left he has the 
right shoulder of his companion and the flowing water. ^ ^ 


\With drawings] 

The small boats in use among the Assyrians were made of thin 
branches of willow, plaited over rods also of willow, arranged in the 
shape of a small boat, plastered over with fine dust soaked in oil or tur- 
pentine and so reduced to a state of mud; this was impervious to water 
and was not cleft asunder by blows because it always remained supple. 

Caesar covered this kind of small boat with oxhide when crossing 
the Sicoris, a river of Spain, according to the testimony of Lucan.^ 
\With drawing 

The Spaniards, the Scythians and the Arabs, when they wish to con- 
struct a bridge very quickly, bind the hurdles formed out of willow upon 
bags or wine-skins of oxhide, and so cross in safety. 62 v 

The Germans, in order to asphyxiate a garrison, use the smoke of 
feathers, sulphur and realgar, and they make the fumes last seven and 
eight hours. 

The chaff of corn also makes fumes which are thick and lasting, as 
does also dry dung; but cause it to be mixed with that is with the 
pulp of crushed olives, or, if you prefer it, with the dregs of the oil. 

B 63 V. 

\With drawing] 

How to discharge a torrent of water on the back of an army and the 
bridges and walls of a town. 

If you wish to submerge a battlefield or to break through walls with- 
out the use of cannon and have the use of a river, do as is represented 
above. That is you set piles as high as the bank of the river and put them 
half a braccio apart or farther if you have wider planks; then set these 
planks between each of the piles and so fill up [the spaces]. When these 
are filled up raise the connecting rod M, then a the upper part of the 
plank will go forward and b the lower part of the plank will go back. In 

^ The reference is to Lucan’s Pharsalia IV, 1 30, etc. 

Utque habuit ripas Sicoris camposque reliquit, 

Primum cana salix madefacto vimine parvara 
Texitur in puppim, caesoque inducta iuvenco 
Vectoris patiens tumidum superenatat amnem. 


this way the parts of the said plank will be edgewise and the water will be 
free to escape. And make the sluices all to open at the blow of a carbine or 
other signal so that they may all open at the same time, in order that the 
flow of the water upon the object which opposes it may be driven by a 
greater blow and a more impetuous force. And if the river have a steep 
descent make one of these every half mile, and let each of the panels open 
by means of a rope to insure them working together, and in order that he 
who unlocks them may be in safety. bS^t 

[With drawing 


If you should be making a bastion at night and have need of light, 
place these lights inside lanterns and raise them up on the top of long 
poles, in order that the enemy by firing at the lights may not touch the 
sappers. And the lights should be of oil so that they may last some time, 
and the lanterns should be balanced in lamp-stands in this way [drawing 
in text\ so that they do not upset when they are raised. And remember 
that the poles must be painted black and only erected at sunset, so that 
the light is scarcely visible and the raising of it up is hardly seen by the 
enemy. And it should be done as noiselessly as possible, and there should 
be one overseer with a staff for every five sappers, so that the work may 
be rapid. 

“ B 70 r. 

In what way one may storm a bastion which has been made in order 
to close a passage. 

Make portable sections of bastions for a furious attack by the men; 
these should be filled with hay and they should be pointed in front in 
order that the blows of the artillery may do no damage, and joined to- 
gether so as to make the bastion of such a size as to engage all the mouths 
of the artillery and the discharge from the bridges, they will be able to 
engage the enemy with advantage. ^ ^ ^ ^ 

[How to attack a fortress by subterranean galleries^ [With drawings]^ 

Rod filled with rockets for encountering the enemy at the outlet of 
a subterranean gallery [that opens] from below upwards, which will 
clear the ground of the men within the entrance. 

Rod with rockets for placing in a gallery that leads into a cellar 
which would be in a fortress and would be well guarded. 

20 % 


m a b. The way of a winding gallery that will deceive the enemy 
when besieged. 

We can clearly understand that all those who find themselves be- 
sieged, employ all those methods which are likely to lead to the discovery 
of the secret stratagems of the besieger. You therefore who seek by 
subterranean ways to accomplish your desire, reflect well how your 
enemy will be on the alert, and how if you should make a gallery on one 
side he will make a trench up to your [gallery], and this will be well 
guarded by day and by night, for it will be supposed that the secret way, 
as is natural, has its outlet in the said gallery. 

When therefore by your digging operations you show that you wish 
to come out in one particular spot, and by making the circuit of the 
fortress you come out at the opposite side, as it is shown above in mb a^b 
will be when you are almost at the outlet in a cellar that is a. You will 
have a great reserve of men who on the breaking of the wall that is 
between you and the cellar ... 

When you have made your gallery almost to its end and it is near to a 
cellar, break through suddenly and then thrust this [rod] in front of you 
filled with rockets if you find defenders there, but if not do not set fire 
to them lest you make a noise. b 78 r 

[Wk/i drawings] 

Stlocladle. Place in the centre powder formed of dried fungi. 

These balls filled with rockets are to be thrown within the bastions 
of the enemy. 

The stlocladle is a ball a foot wide which is made up of hemp and 
fish-glue and is covered with the tails of rockets, and these tails do not 
exceed in length the length of a finger, and each tail is of fine copper 
veined or of sized pasteboard, and all the said tails have their extremities 
pierced by a tiny hole, and they are all attached to a copper ball which is 
full of many paths after the manner of a labyrinth, filled with powder; 
and the said paths are full of holes that cross them which meet with the 
holes of the rockets. 

Then one sets fire to it by means of a bellows and the fire hurls itself 
through eight holes so that no one can control it or . . . \ariegiT]^ and when 
the fire has penetrated to the centre the rockets begin suddenly one after 
another with a dreadful din to spit forth their deadly missiles. If you 
wish to make use of it on a galley make the rockets of pasteboard, and 



■fill the space between each with pitch mixed with powdered sulphur; 
and this will serve three purposes: first it will do harm with the rockets, 
second it will kindle a fire there which cannot be put out, and will burn 
the wood, and (third) no one will be able to approach it because of the 
great stench. 

Buffonico, The buffonico is an instrument set at the end of a lance. 
It is two braccia long and an eighth of a braccio thick. It is shod with 
iron and has a thin tube with the sight placed on the extremity through 
which it passes to the fire. 

First of all fill the cannon with the powder well crammed, pressed, 
and beaten through the mouth a then make a small hole an eighth of a 
braccio long and insert a small tube with a very fine hole. The powder 
should be fine and mixed with dust of lead made with a file or by 
fire; and it will cause great terror and loss to the horses and to the 


Vinea. The vinea is a machine which makes the road and levels the 
embankments. bSzv 

\JVith drawing of tanJi\ 

These take the place of the elephants. One may tilt with them. One 
may hold bellows in them to spread terror among the horses of the 
enemy, and one may put carabineers in them to break up every 
company. ^ 


This is proved by the ninth, ‘Concerning Percussion’, which says: 
of things movable, in proportion to the power of the mover and the 
resistance of the medium, that which in like movement strikes with a 
larger part of itself will make a louder noise and a less violent impact; and 
that on the other hand which strikes with a less part of itself will make a 
less noise and penetrate farther into the place where it has struck. An 
example has been cited of a sword striking first with the flat and then 
with the edge, for in the one case the stroke makes a great noise and 
penetrates a very little way and in the other it penetrates a long way and 
makes but little noise. As the flame therefore is in proportion to the 


projectiles driven by the pieces of ordnance which are thus in the 
medium proportioned to them, that flame which separates least after 
emerging from the piece of ordnance will be that which will drive the 
ball out with most impetus, and the flame that separates rapidly will do 
the contrary. 


A piece of ordnance which throws a ball a distance proportionate to 
its force, will in the same time throw six of the same balls a sixth part of 
the aforesaid distance. 

E 27 V. 


Of the chambers or receptacles for powder of pieces of artillery one 
finds three varieties of shapes; of which one is wide at the bottom and 
narrow at the mouth; another narrow at the bottom and wide at the 
mouth; the third is of uniform width. 

There are four [?five] places at which one sets fire to pieces of artillery. 
Of these one is the extreme upper part of the bottom of the chamber; 
another is at the middle of the bottom of this chamber; the third is 
as far removed from the bottom of this chamber as half the diameter of 
the circle of this bottom; the fourth receives the fire in the same position 
as the third but in the centre of the thickness of the powder; in the fifth 
the chamber is round and the fire is set in the centre of the chamber. 
But this instrument and the others which set the powder alight in very 
quick time ought to be of fine substance and well compressed. This 
compression occurs very rarely when the cast is of great thickness, because 
in the case of these the metal remains liquid longer in proportion as they 
are thicker, and because the parts of it which are most distant from the 
centre of this thickness are those which are compressed first. ^ 28 r. 

[Ancient military terms\ 

Chiliarch — captain of thousand 
Prefects = captains 


\0f the trajectory of a bombard\ 

If a bombard hits a mark in a straight line at ten braccia how far 
will it fire at its greatest distance? 

And so conversely if it fires three miles at its greatest distance how 
far will it carry in a straight line? 

If a bombard fires at different distances with different curves of 
movement, I ask in what section of its course will the curve attain its 
greatest height. .i^srsolv. 


If with its maximum power a bombard throws a ball of a hundred 
pounds three miles, how far will it throw one of two hundred or three 
hundred or any other weight more or less than a hundred? 

If a bombard with four pounds of powder throws a ball weighing 
four pounds two miles with its maximum power, by how much ought I 
to increase the powder for it to carry four miles? 

If with four pounds of powder a bombard hurls a ball of four pounds 
two miles how far will six pounds of powder hurl it? ^ ^ 

Of the movement of the cannon-balls of bombards, and of the nature 
of the stock and breech of these bombards. 

Whether the ball moved by force will have a greater movement than 
that which is moved with ease or no. 

Whether if a bombard can throw a ball of a hundred pounds it is 
better to put two balls of fifty pounds for one and make the stock narrow, 
or rather with the stock wide to throw one ball of a hundred pounds. 

If the bombard can throw two or three balls with ease I ask whether 
it is better to make the ball long or no. 

If a bombard throws a weight of a hundred pounds a distance of a 
mile, how far will it throw a hundred balls of one pound at one 

Whether it is better for the bombard to be narrow at the mouth and 
wide at the foot, or narrow at the foot and wide at the mouth. 

1 133 [85] V. 

If the bombard rests on the ground or a stump, or straw or feathers, 
what difference will there be in the recoil? 


If two bombards can be fired in opposite directions if the breach of 
the one be placed against that of the other in a straight line, 



If the bombard is fired at sea or on the land what difference there 
will be in its power. 

What difference there is between the movements made upwards or 
crosswise, or in damp or dry weather, or when it is windy or rainy or 
with snow falling, either against or across or in the direction of the course 

Where the ball makes most rebounds — upon stones, earth or water. 

How the smooth ball is swifter than the rough one. 

Whether the ball revolves in the air or no. 

Of the nature of the places struck by these balls. ^ ^ |-gg^ ^ 

For a bastion to have spring in it, it should have a layer of fresh willow 
branches placed in the soil at intervals of half a braccio. 

'^Powder for a bomb-ketch\ 

One pound of charcoal 
eleven ounces of sulphur 

^nd^mtek well aL moisten it with good brandy, and dry it in 
the sun or at the fire. Then pound it until one cannot see a speck of 
sulphur or saltpetre but it is all black and umform and fine, and moisten 
it again with tL brandy and keep it so. Dry it in the ^ 

cruli just so much as can be placed upon the hole, and this will be 

sufficient. ^ + 

[For digging trenches] 

nkre men according to the marks shown. And first of all make tn 
Lcavation as far as possible from the place where the earth is tossed. 
For Ixample the earth is excavated at it g, it is carried along the me 
r c unloaded by the line cf, and then the man turns back along the fine 

soil from the place where the fine rcis marked. 

jife wall fifteen feet thick at the base and thirteen above, 


L 24 r. 


The trench forty two braccia wide at the bottom, fifty at its mouth; 
twenty braccia in height, with water four braccia deep. l 29 r 

Fifteen steps and a span from the battlements to the water, that is 
from the beginning of the battlements, and these steps are the distance 
from one extremity of the palms of the hands to the other, opening them 
as far as one can upon a rectilineal measure. And there are eight braccia 
and a sixth from the said beginning of the battlements to the summit of 
the turret. l67v. 

[Of digging a trencK\ 

Width of trench and its depth. Diameter of wheel and thickness of 
beam and cord. And position of men who turn it and number of men 
who work this wheel. How many there are in position and what weight 
they draw at one time, and how much time is required to fill and move 
in order to empty and turn, and similarly how many shovelfuls one 
man digs out in an hour, and what a shovelful weighs, and how far he 
throws it away from himself either upwards, across or downwards, beyond 
thehUlock. j, cover r. 

Which will fire the farthest, powder double in quantity or in quality 
or in fineness.? 



Plan of drawbridge which Donnino showed me. 

And because c and d drive downwards, the space a b becomes twisted, 
consequently it ought to be strengthened by a thick iron bar bent over 
the wood on the opposite side. ^ ^ 

[Bombards and cross-bows] 

If the bombard has a recoil of a quarter of a braccio how much will 
it lose in front of its true and suitable range.? 

If the unlocking of the cross-bow is made with the cross-bow fixed or 
driven forward or drawn back, what will it lose or gain upon its natural 

Which of these bombards throws farthest and how far? 



\Breeches of bombards\ 

That part of the bronze is most compressed within its mould which is 
most liquid. 

And that is most liquid which is hottest, and that is hottest which 
comes first out of the furnace. One ought therefore always to make first 
in the casting that part of the cannon which has to receive the powder 
before that which has to contain the muzzle. 

A long breech is an embarrassment and filljj^p space uselessly and 
unserviceably and causes loss of speed. 

•' ^ M 54 V. 


If you wish to find out where a mine runs set a drum over all the 
places where you suspect the mine is being made and on this drum set a 
pair of dice, and when you are near the place where the mining is the 
dice will jump up a little on the drum, through the blow given under- 
ground in digging out the earth. 

There are some who having the advantage of a river or swamps upon 
their land have made a great reservoir near the place where they suspect 
that the mine may be made, and have made a tunnel in the direction of 
the enemy, and having found them have unlocked the waters of the 
reservoir upon them and drowned a great number of people in the mine. 

M.8. 2037 Bib. Nat i r. 

The shields of footsoldiers ought to be of cotton spun into thread 
and made into cords; these should be woven tightly in a circle after the 
fashion of a buckler. 

And if you so wish the threads should be thoroughly moistened 
before you make cords of them, and then smeared with the dross of iron 
reduced to powder. 

Then plait it in cords a second time with two, then with four, then 
with eight, and soak them every time in water with borax or linseed or 
the seed of quinces. And when you have made your cord weave the 
shield. And if you make a doublet let it be supple, light and 
impenetrable. „s. 2037 Bib. Nat. 7 r. 

If it should happen when a town is besieged that the mines made by 
the enemy have not penetrated within it, you should place men with the 
greatest possible care at intervals of ten braccia in that quarter in which 
your suspicions centre, with their ears on the ground, and as soon as the 



0 2 


tremor of the sound reaches them, let them make a very deep trench 
crosswise, which will be ready to swallow up the mine when it comes 
upon it. Then have ready a vessel of iron or copper perforated at the 
bottom, and in the hole have placed the nozzle of a smith’s bellows, 
and then cover over the mouth with a plate of iron, perforated in many 
places, and fill it with fine feathers; and you turn the mouth in the 
direction of the mine when it is discovered and blow with the bellows, 
after having first caused the bellows to be mixed with sulphur and 
burnt, and the smoke that issues forth will drive away the enemy. 

If however you do not wish to make the above-named trench within 
the circuit of the walls, in order not to interfere with the rounds of the 
soldiers who are defending the walls, you should make a drill as was 
shown above, and with this at intervals of two braccia you make a hole 
six braccia in depth, and make these in a circular line within the walls 
following the circle of the walls, and let it be as long as you suspect the 
mine to be. And every hour you excavate these holes one by one and 
measure them afresh within with a rod, comparing with them the former 
measurements of the holes, and if the rod should sink down then know 
that the mine is there and cause them to dig there and there make your 

Or if you do not wish to make the test with the rod in order to 
discover a mine, go every hour with a light above each hole, and when 
you come to the hole which is above the mine the light will be imme- 
diately extinguished. 5 ^ 

When besieged by ambitious tyrants I find a means of offence and 
defence in order to preserve the chief gift of nature, which is liberty; 
and first I would speak of the position of the walls, and then of how the 
various peoples can maintain their good and just lords. 

MS. 2037 Bib. Nat. lo r. 

Of the power of the bombard and the resistance of the object struck, 
that is that the ball will subdue a wall of one braccio and of two braccia 
and so of any thickness. Forster., 6 r. 


Prove in the model of the mangonel, which does not become 
exhausted as does the cross-bow, and mark with the same weight to 
what distances the different weights thrown by it are carried, and 



further in respect of the throwing of the same weight see how to vary 
the counterpoise for the mangonel. 

Remember that the more powder there is in the carbine the more the 
length of the barrel is diminished, so that you have to pay attention to 
the proportions of your forces, „ ^ 

^ ^ J Forster n 39 r. 

If you wish to escape from a city or other closed-in place, fill the 
door-lock with powder from the carbines and set fire to it; also when 
about to scale walls it will be useful in driving the enemies from the 
battlements with its blaze, „ ^ 

rorster II 49 r. 

What substance is it which offers most resistance to the percussion of 
the bombard, i.e, to its passage? 


Length ten braccia; ball an inch thick and ten long; the shape 
should taper somewhat. Forster u 56 v. 


That bombard discharges its ball to the farthest distance from itself 
which breaks its obstacles most. Forster n 57 r. 

Of the bombards narrow at the base and wide at the mouth, and so 
of those straight and those curved, and similarly of the tails narrow at 
the end and wide at the mouth; and the proof is by the flames when it is 
discharged. Forster.. sSr. 


Make a rule to apply to every description of ball, of iron as of lead 
or stone, how you ought to increase or diminish the amount of powder, 

Forster n 62 r. 


Of many bombards equal in respect of powder and ball, that from 
which in equal time there is kindled a greater quantity of fire, will hurl 


Of balls of equal weight that which is the swifter will seem 
heavier and will produce a greater percussion. Forster n 71 r 

If the bombard has its stone flattened like a cheese, and the hollow 
of the bombard has a like shape, and the centre — the centre of the tail — 
does not encounter the centre of the stone, so that it goes revolving 
through the air, it will undoubtedly be exceedingly swift. 

For if you take a ball of six ounces and a wheel of like weight 
without angles at its edges, you will see how much greater a distance the 
one will be sent by its mover than the other; and this is also due in part 
to the revolving of its additional substance. And this happens because 
as the balls are equal in weight, from being round it strikes more air 
and finds more resistance, and from being flattened it enters upon the 
air edgewise and penetrates it more rapidly, and more rapidly moves 
through it. Forster n 73 r. 

\War Machines: ’with drawing 

When this is going through its own ranks, it is necessary to raise 
the machinery that moves the scythes, in order to prevent their doing 
any harm to anyone. 

How the armoured car is arranged inside. 

It will need eight men to work it and make it turn and pursue the 

This is good to break through the ranks, but it must be followed up. 

B.M. Drawings 



Naval Warfare 



\Notes relating to a submarine attac}(\ 

Do not impart your knowledge and you will excel alone. 

Choose a simple youth and have the dress stitched at home. 

Stop the galleys of the captains and afterwards sink the others and 
fire with the cannon on the fort. 

\With drawings of parts of the apparatus^ 

Everything under water, that is all the fastenings. 

Here stands the man. Doublet. Hose. Level frame. 

JVith drawing of small boat under poop of large^ 

When the watch has gone its round, bring a small skiff under the 
poop and set fire to the whole all of a sudden. 

\With drawing of boat and chain\ 

To fasten a galley to the bottom m on the side opposite to the anchor. 
\fVith drawing of figure in diving dress {half length)] 

A breastplate of armour together with hood, doublet and hose, and 
a small wine-skin for use in passing water, a dress for the armour, and 
the wine-skin to contain the breath, with half a hoop of iron to keep it 
away from the chest. If you have a whole wine-skin with a valve from 
the [.?ball da pal . . . fpalla) you deflate it, you will go 

to the bottom, dragged down by the sacks of sand; when you inflate it, 
you will come back to the surface of the water. 

A mask with the eyes protruding made of glass, but let its weight 
be such that you raise it as you swim. 

Carry a knife which cuts well so that a net does not hold you prisoner. 
Carry with you two or three small wine-skins, deflated, and capable of 
being inflated like balls in case of need. 

Take provisions as you need them, and having carefully wrapped 
them up hide them on the bank. But first have an understanding about 
the agreement, how the half of the ransom is to be yours without deduc- 
tion; and the store-room of the prisons is near to Manetti, and payment 
may be made into the hand of Manetti, that is, of the said ransom. 

Carry a horn in order to give a signal whether or no the attempt has 
been successful. 

You need to take an impression^ of one of the three iron screws of the 

MS. has ■protare for which Piumati in his transcript of the Codice Atlantico reads 
portare. I have adopted Muller-Walde’s reading, prontare for improntare. 

■ 215 ■ 


workshop of Santa Liberata, the figure in plaster and the cast in wax. 
[With drawing of figure of man in diving dress. His right arm extended 
holds a staff which touches a square of cork. Two bags suspended from 
shoulder s^ 

It separates from the dress if it should be necessary to break it. 

Cork which is to be fixed midway between the surface and the 

Bags of sand. 

Carry forty braccia of rope fastened to a bag of sand.^ 

C.A. 333 V. a 

I will destroy the harbour. 

Unless you surrender within four hours you will go to the bottom. 
[Notes with drawings of three heads showing diving apparatus fitted 
over the nostrils'] 

Have the said bag for your mouth ready for use when you are in 
the sea — for was not this your secret.? 

Try it first for four hours. 


Of bronze, which is fastened with a screw that has been oiled, it 
should have been made in a mould. . 

C.A. 346 r. a 

[Drawing of buoy, below which, connected by a long bar, that moves freely 
on swivels, hangs what is apparently a very large awl or borer. At 
the side of the buoy a long tube is fastened so that one end projects 
just above it', it is bound by a number of rings, and its lower end 
terminates in a sort of bag, which is apparently fixed over the mouth 
of the diver. A dotted horizontal line shows that this is level with the 
top of the borer] 

Line to find the middle. 

In case you have to make use of the sea make an armour of copper 

^ Alvise Manetti was sent by the Venetian senate on a legation to the Turks, which 
lasted from October 1499 to the end of March 1500, to attempt some arrangement 
for the surrender of the Venetian prisoners who were removed from Constantinople to 
Lepanto after the capture of that fortress by the Turks in August 1499. Already in 
February 1500 a despatch from Manetti had arrived in Venice which showed that his 
endeavours were not likely to reach a successful issue. It was presumably at about this time 
that Leonardo, who was then in Venice, set himself to devise some method of securing the 
release of the prisoners through the agency of Manetti, and also to consider a plan for 
destroying the enemy’s ships in the harbour by piercing them below the water-line. 



by setting the plates one above another thus: \drawin^. That is, one 
inside the other, so that a hook may not grapple you. 

Measure first the depth, and if you see that it will be sufficient merely 
to bore without sinking the ship, pursue that course; otherwise fasten it 
in the way indicated. 

Hole by which the water makes its exit when the ring is lowered. 

Oars. Twelve braccia the lever. Twelve braccia. For the final turn 
you need a bent lever. In order to turn this screw use a pair of slippers 
with heels, or hooks, so that the foot may stand firm. 

These are the implements which belong to it; but construct it so that 
the wine-skin which serves as a boat, and the implements and the man 
who is there, shall be midway between the surface and the bottom of 
the sea; and have a valve put in this wine-skin, so that when it is deflated 
it will sink to the bottom where your station is, and the hands will serve 
as oars. 

The way of wings. 

The smoke of [. . .] for use as an opiate. 

Take seed of darnel as remedy, and [. . .] spirits of wine in cotton. 
Some white henbane. Some teasel. 

Seed and root of ntappello\(\^'^ and dry everything; mix this powder 
with camphor and it is made. 

Deadly smoke {fumo mortak)'. 

Take arsenic and mix with sulphur or realgar. 

Remedy rose water. 

Venom of toad, that is, a land-toad. 

Slaver of mad dog and decoction of dogwood berries. 

Tarantula from Taranto. 

‘Powder of verdigris or of chalk mixed with poison to throw on ships, 

C.A. 346 V. a 


Take charcoal of willow, and saltpetre, and aqua vitas, and sulphur, 
pitch, with incense and camphor and Ethiopian wool, and boil them all 
up together. This fire is so eager to burn that it will run along wood 
even when it is under water. You should add to the mixture liquid varnish, 
petroleum,’- turpentine, and strong vinegar, and mix everything together 

^ Mappello^ ^xi as yet unidentified tree or shrub. In a passage in c.a. 214 r. a it is said 
to grow plentifully in the Valsasina, which is to the south of Lake Como. 


■ ■ .217 


and dry it in the sun or in an oven when the bread has been taken out, 
and then stick it round hempen or other tow, moulding it to a round 
form and driving very sharp nails into every side of it. Leave however 
an opening in this ball to serve for a fuse, and then cover it with resin 
and sulphur. 

This fire moreover, when fixed to the top of a long lance, which has a 
braccio of its point covered with iron in order that it may not be burnt 
by it, is useful for avoiding and warding off the hostile ships in order not 
to be overwhelmed by their onset. 

Throw also vessels of glass filled with pitch on to the ships of the 
enemy when their crews are engaged in the battle, and by then throwing 
similar lighted balls after these you will have it in your power to set every 

ship on fire. ^ 

^ Tr. 43 a 

Ships made of beams. 

Ships made of osier twigs woven and bound with leather for priva- 
teers. ■ 

In order to fight against walls which face the sea or towers, withdraw 
the galleys, and before they come to the encounter raise the oars within 
so that the edges touch together, and move the ship with the oars of the 
back part; in this manner it will seem one only, upon which you will set 
tower and fort strong and suitable for carrying any artillery that will 
be serviceable for the battle. ' 

, , Tr. 71 a 


These cortalds should be placed upon stout ships, and these two 
cortalds will have ~ fastened by a strong chain or a new rope soaked in 
water — a scythe twelve braccia long and a foot wide at the centre, and 
with the back of the blade of the thickness of a finger; and one ought to 
be able to fire both of them at the same time. 


[With drawing 

To throw poison in the form of powder upon galleys. 

Chalk, fine sulphide of arsenic, and powdered verdigris may be 
thrown among the enemy ships by means of small mangonels. And all 
those who, as they breathe, inhale the said powder with their breath 
will become asphyxiated. 

But take care to have the wind so that it does not blow the powder 


\With drawing 

Lances of considerable length fitted with short rockets should be 
placed within the edges of the ships, and these may be set on fire by 
means of a thin cord which comes down the length of the pole as far as 
the hand. ■ n, ■ 


\With drawing 

It is necessary first that they be engaged, that is fastened together in 
such a way that you for your part can unlock yourself at your pleasure, 
so that when the ship goes to the bottom it may not drag yours with it. 
Let this be done as follows: — draw a weight up to a height and then 
release it; and as it falls it will give such a blow as a pile-driver gives, and 
in falling it will draw back the head of a beam which is in equilibrium 
when upright, and as the head of the aforesaid beam comes back the 
end that is below advances and staves in the bow of the ship. But see to 
it that the beam has a cutting edge so that as it rushes to give the stroke 

back upon you, or to have your nose and mouth covered over with a fine 
cloth dipped in water so that the powder may not enter. It would also 
be well to throw baskets covered with paper and filled with this powder 
from the crow’s nest or the deck of the ship. 

^ B 69 V. 

\With drawings'^ 

Ship with scorpions suitable for cutting the ropes of the big ships; 
from one tip of the sickles to the other should be four braccia; and the 
sickle should be of the shape of a crescent, one foot at its maximum 
width and of the breadth of a finger. , 

o - B 76 r. 

[With dramngs\ 

Cir cunful gore. The circunfulgore is a naval machine invented by the 
inhabitants of Majorca. It is formed of a circle of bombards, of as many 
as you please provided that the number is not uneven, since in order that 
the blow may be a vigorous one and yet the vessel may not spring back 
it is necessary that one bombard should serve as a support and obstacle 
of another, and in order to effect this it is necessary to set fire at the same 
instant to two bombards placed opposite to each other, so that if one 
wishes to flee on one side the other opposes it. b 82 v 


the water does not offer resistance to it. And above all see that the chains 
which hold the ships fastened together are such as can at your pleasure 
be severed from your side, so that the enemy’s ship when it sinks may 
not drag you down with it. b o v 


If in a battle between ships and galleys the ships are victors because 
of the height of their mast-heads, you should draw the lateen yard almost 
up to the top of the mast and attach to the extremity of this yard — ■ at 
the end that is which projects towards the enemy — a small cage wrapped 
at the bottom and all round with a large mattress stuffed with cotton 
to prevent it from being damaged by bombs. 

Then draw down the other end of the lateen yard by means of the 
capstan, and the cage at the opposite end will go up to such a height that 
it will be far above the mast-head of the ship, and you will easily be able 
to drive out the men who are within it. 

But it is necessary that the men in the galley should go to the 
opposite side so that they may counterbalance the weight of the men 
posted in the cage of the lateen yard. 


If you wish to build a fleet for action you should make use of these 
ships in order to ram the enemy’s ships, that is, make ships a hundred 
feet^ in length and eight feet wide and arrange them so that the rowers 
of the left oars sit on the right side of the ship and the rowers of the right 
oars on the left side, as is shown at M {figure), in order that the leverage 
of the oars may be longer. And this ship should be a foot and a half in 
thickness, that is made of beams fastened inside and outside by planks 
set crosswise. 

And let the vessel have fastened to it a foot below the water’s 

edge a spike shod with iron of the weight and size of an anvil. And 
by the might of the oars this vessel will be able to draw back after it 
has struck the first blow, and will then hurl itself forward again with 
fury and deal the second blow and then the third, and so many others 

as to destroy the ship. 

MS. 2037 Bib. Nat. 3 r. 

^ Dimensions here given in feet, more usually in braccia. According to Fanfani’s 
Dictionary, a foot was about 30 centimetres, and a braccio (fiorentino) was 58 centimetres. 

■ 32Q : ■ 



Shape of the vessel [?bomb-ketch] which carries the mortars described 
above. And I would specially remind you to aim the cannon-balls 
attached to scythes towards the mast-head where many ropes unite and 
where the scythes will be effective. 

The scythes should be four braccia long and four braccia from one 
point to the other. And they should be shot among the ropes of the big 
ships so as to make the sails fall down. And let the ketch which carries 
them carry a sufficient quantity; and let it be of stout beams so that the 
cannon from the ships may not break them in pieces; and let the cannon- 
balls be of two hundred pounds. ^ 

r MS. 2037 Bib. Nat. 4 v. 


Of the means of defence in case the enemy should throw soft soap, 
or caltrops, or small boards studded with nails, or similar things upon 
the ships. 

You should do thus; — keep, when you go into the combat, on your 
feet, underneath your shoes, iron soles, divided in the middle as is shown 
in the drawing above, so that it is possible to bend the feet; and the 
underside of these soles should have the form of a rasping file, or be filled 
with blunted points of nails, in order to prevent the soap from causing 
the foot to slip and so making the man fall down flat; and, as they are of 
iron, the small boards and caltrops will be thrown in vain. 

MS. 2037 Bib. Nat. 6 v. 



This machine is so constructed that the scythe springs up when it is 
discharged; and the ships which carry scythes should be of this sort, 
namely without either mast or sail and with a great quantity of oars so 
that they may be swift; without a sail because the sail, mast and cordage 
would interfere with the working of the great scythe. The machine is 
called a scorpion because of its resemblance to one and because of the 
damage it inflicts with its tail. Mantelets are fixed over the rowers in 
order that the masts, that is to say the mast-heads, or rather the combatants 
at the mast-heads, may not be able to do them any injury; and these 
should be covered with moist hides because of the fire thrown by the 


A way of protecting against it is for ships to be provided with chains 
of rope to a height of six braccia. 

[Figure] This ship is to serve as a defence against cannon, and it 
attacks the other ships with its cannon; it is covered with sheet metaL 
as a protection against fire, and bristling with points of nails so that the 
enemy may not leap upon it with impunity. 3 ^ 


Some of the combatants in the Tyrrhenian Sea employ this method: 
they fasten an anchor to one end of the lateen yard and a rope to the 
other, and this rope at the bottom end is attached to another anchor. 
In the fight they hook the first anchor to the oars of the enemy’s ship 
and by the force of the capstan draw it to the side. 

And they throw soft soap and tow, dipped in melted pitch and set 
alight, on the side to which the anchor was first made fast, so that in order 
to escape from this fire the defenders of the ship have to flee to the 
opposite side; and by doing so they rendered assistance to their assailants, 
for the galley was drawn to the side more easily because of this counter- 

MS. 2037 Bib. Nat. 9 r. 


I have found in the histories of the Spaniards how, in their wars with 
the English, Archimedes the Syracusan, who was then living at the court 
of Ecliderides, King of the Cirodastri, ordered that for maritime combats 
the ships should have tall masts, and on the tops of these he placed a 
small yard forty feet in length and a third of a foot wide, having at one 
end of it a small anchor and at the other a counterpoise. 

To the anchor was attached twelve feet of chain, and to the chain as 
much rope as would reach from the chain to the base of the mast-top 
where it was fixed by a small rope, going down from this base to the 
base of the mast where a very strong capstan was placed, and there the 
end of the cord was fastened. But to go back to the use of the machine, 
I say that below this anchor there was a fire which with a loud roar 
threw out its rays and a shower of burning pitch, and as this shower fell 
upon the enemy’s mast-top it compelled the men stationed there to 
abandon their post; and consequently the anchor being lowered by 
means of the capstan touched the sides of the mast-top, and thus 
^ MS. coperto di tole. 



instantly cut the rope placed at the base of the mast-top to support the 
rope which went from the anchor to the capstan. And drawing the 
ship ... 

MS. 2037 Bib. Nat. 9 v. 

How by an appliance many are able to remain for some time under 
water. How and why I do not describe my method of remaining under 
water for as long a time as I can remain without food; and this I do not 
publish or divulge on account of the evil nature of men who would 
practice assassinations at the bottom of the seas, by breaking the ships in 
their lowest parts and sinking them together with the crews who are in 
them; and although I will furnish particulars of others they are such as 
are not dangerous, for above the surface of the water emerges the mouth 
of the tube by which they draw in breath, supported upon wineskins 
or pieces of cork. ^ 

Leic. 22 V. 

Speak with the Genoese about the sea. 2 

1 These lines are an excerpt from a passage to be found in full in the section on The 
Nature of Water. A similar practice has been followed in the case of one or two lines 
reproduced in the sections entitled Music, Personalia and Dated Notes. 

® This is one of those enigmatic notes which have given rise to conjecture. It un- 
doubtedly may refer to naval preparations, which were being taken by the Genoese as 
part of Ludovic Sforza’s concerted schemes of defence against the assaults with which 
he was threatened. As he knew of Leonardo’s study of marine warfare he would find 
him a very suitable agent to send on such a mission. This is incontestable. But the 
fact remains that this sentence, which is all that exists to connect Leonardo with Genoa, 
is a comparatively slight foundation for the structure of hypothesis that has been raised 
upon it. 


Comparison of the Arts 

.‘If you know how to describe and write down 
the appearance of the forms, the painter can 
make them so that they appear enlivened with 
lights and shadows which create the very 
expression of the faces; herein you cannot attain 
with the pen where he attains with the brush.’ 

How painting surpasses all human works by reason of the subtle 
possibilities which it contains: 

The eye, which is called the window of the soul, is the chief means 
whereby the understanding may most fully and abundantly appreciate 
the infinite works of nature; and the ear is the second, inasmuch as it 
acquires its importance from the fact that it hears the things which the 
eye has seen. If you historians, or poets, or mathematicians had never 
seen things with your eyes you would be ill able to describe them in 
your writings. And if you, O poet, represent a story by depicting it 
with your pen, the painter with his brush will so render it as to be more 
easily satisfying and less tedious to understand. If you call painting 
‘dumb poetry’, then the painter may say of the poet that his art is ‘blind 
painting’. Consider then which is the more grievous affliction, to be 
blind or to be dumb! Although the poet has as wide a choice of subjects 
as the painter, his creations fail to afford as much satisfaction to mankind 
as do paintings, for while poetry attempts to represent forms, actions and 
scenes with words, the painter employs the exact images of these forms 
in order to reproduce them. Consider, then, which is more funda- 
mental to man, the name of man or his image? The name changes with 
change of country ; the form is unchanged except by death. 

And if the poet serves the understanding by way of the ear, the 
painter does so by the eye, which is the nobler sense. 

I will only cite as an instance of this how if a good painter represents 
the fury of a battle and a poet also describes one, and the two descrip- 
tions are shown together to the public, you will soon see which will draw 
most of the spectators, and where there will be most discussion, to which 
most praise will be given and which will satisfy the more. There is no 
doubt that the painting, which is by far the more useful and beautiful, 
will give the greater pleasure. Inscribe in any place the name of God 
and set opposite to it His image, you will see which will be held in greater 

Since painting embraces within itself all the forms of nature, you have 
omitted nothing except the names, and these are not universal like the 
forms. If you have the results of her processes we have the processes of 
her results. 

Take the case of a poet describing the beauties of a lady to her lover 


and that of a painter who makes a portrait of her; you will see whither 
nature will the more incline the enamoured judge. Surely the proof of 
the matter ought to rest upon the verdict of experience! 

You have set painting among the mechanical arts! Truly were 
painters as ready equipped as you are to praise their own works in 
writing, I doubt whether it would endure the reproach of so vile a name. 
If you call it mechanical because it is by manual work that the hands 
represent what the imagination creates, your writers are setting down 
with the pen by manual work what originates in the mind. If you call 
it mechanical because it is done for money, who fall into this error — if 
indeed it can be called an error — more than you yourselves? If you 
lecture for the Schools do you not go to whoever pays you the most? Do 
you do any work without some reward? 

And yet I do not say this in order to censure such opinions, for every 
labour looks for its reward. And if the poet should say, T will create a 
fiction which shall express great things’, so likewise will the painter also, 
for even so Apelles made the Calumny. If you should say that poetry 
is the more enduring, — - to this I would reply that the works of a copper- 
smith are more enduring still, since time preserves them longer than 
either your works or ours; nevertheless they show but little imagination; 
and painting, if it be done upon copper in enamel colours, can be made 
far more enduring. 

In Art we may be said to be grandsons unto God. If poetry treats 
of moral philosophy, painting has to do with natural philosophy; if the 
one describes the workings of the mind, the other considers what the 
mind effects by movements of the body; if the one dismays folk by 
hellish fictions, the other does the like by showing the same things in 
action. Suppose the poet sets himself to represent some image of beauty 
or terror, something vile and foul, or some monstrous thing, in contest 
with the painter, and suppose in his own way he makes a change of forms 
at his pleasure, will not the painter still satisfy the more? Have we not 
seen pictures which bear so close a resemblance to the actual thing that 
they have deceived both men and beasts? 

If you know how to describe and write down the appearance of the 
forms, the painter can make them so that they appear enlivened with 
lights and shadows which create the very expression of the faces; herein 
you cannot attain with the pen where he attains with the brush. 

MS. 2038 Bib. Nat. 19 r. and V., 20 r. 


How he who despises painting has no love for the philosophy in 

If you despise painting, which is the sole imitator of all the visible 
works of nature, it is certain that you will be despising a subtle invention 
which with philosophical and ingenious speculation takes as its theme all 
the various kinds of forms, airs and scenes, plants, animals, grasses and 
flowers, which are surrounded by light and shade. And this truly is a 
science and the true-born daughter of nature, since painting is the off- 
spring of nature. But in order to speak more correctly we may call it 
the grandchild of nature; for all visible things derive their existence from 
nature, and from these same things is born painting. So therefore we 
may justly speak of it as the grandchild of nature and as related to God 

himself. „ 

MS. 2038 Bib. Nat. 20 r. 

That sculpture is less intellectual than painting, and lacks many of 
its natural parts: 

As practising myself the art of sculpture no less than that of painting, 
and doing both the one and the other in the same degree, it seems to me 
that without suspicion of unfairness I may venture to give an opinion as 
to which of the two is the more intellectual, and of the greater difficulty 
and perfection. 

In the first place, sculpture is dependent on certain lights, namely 
those from above, while a picture carries everywhere with it its own 
light and shade; light and shade therefore are essential to sculpture. In 
this respect, the sculptor is aided by the nature of the relief, which pro- 
duces these of its own accord, but the painter artificially creates them by 
his art in places where nature would normally do the like. The sculptor 
cannot render the difference in the varying natures of the colours of 
objects; painting does not fail to do so in any particular. The lines of 
perspective of sculptors do not seem in any way true; those of painters 
may appear to extend a hundred miles beyond the work itself. The 
effects of aerial perspective are outside the scope of sculptors’ work; they 
can neither represent transparent bodies nor luminous bodies nor angles of 
reflection nor shining bodies such as mirrors and like things of glittering 
surface, nor mists, nor dull weather, nor an infinite number of things 
which I forbear to mention lest they should prove wearisome. 

The one advantage which sculpture has is that of offering greater 
resistance to time; yet painting offers a like resistance if it is done upon 


Comparison of the arts 

thick copper covered with white enamel and then painted upon with 
enamel colours and placed in a fire and fused. In degree of permanence 
it then surpasses even sculpture. 

It may be urged that if a mistake is made it is not easy to set it 
right, but it is a poor line of argument to attempt to prove that the 
fact of a mistake being irremediable makes the work more noble. 
I should say indeed that it is more difficult to correct the mind of 
the master who makes such mistakes than the work which he has 

We know very well that a good experienced painter will not make 
such mistakes; on the contrary, following sound rules he will proceed by 
removing so little at a time that his work will progress well. The 
sculptor also if he is working in clay or wax can either take away from it 
or add to it, and when the model is completed it is easy to cast it in 
bronze; and this is the last process and it is the most enduring form of 
sculpture, since that which is only in marble is liable to be destroyed, 
but not when done in bronze. 

But painting done upon copper, which by the methods in use in 
painting may be either taken from or altered, is like the bronze, for 
when you have first made the model for this in wax it can still be either 
reduced or altered. While the sculpture in bronze is imperishable this 
painting upon copper and enamelling is absolutely eternal; and while 
bronze remains dark and rough, this is full of an infinite variety of 
varied and lovely colours, of which I have already made mention. But if 
you would have me speak only of panel painting I am content to give 
an opinion between it and sculpture by saying that painting is more 
beautiful, more imaginative, and richer in resource, while sculpture is 
more enduring, but excels in nothing else. 

Sculpture reveals what it is with little effort; painting seems a thing 
miraculous, making things intangible appear tangible, presenting in 
relief things which are flat, in distance things near at hand. 

In fact, painting is adorned with infinite possibilities of which 
sculpture can make no use. o j . 

MS. 2038 Bib. Nat, 25 V. and 24 v. 

One of the chief proofs of skill of the painter is that his picture should 
seem in relief, and this is not the case with the sculptor, for in this respect 
he is aided by nature. 

J C.A. 305 r. a 


[Of poetry and paintingl 

When the poet ceases to represent in words what exists in nature, he 
then ceases to be the equal of the painter; for if the poet, leaving such 
representation, were to describe the polished and persuasive words of one 
whom he wishes to represent as speaking, he would be becoming an 
orator and be no more a poet or a painter. And if he were to describe the 
heavens he makes himself an astrologer, and a philosopher or theologian 
when speaking of the things of nature or of God. But if he returns to the 
representation of some definite thing he would become the equal of the 
painter if he could satisfy the eye with words as the painter does with 
brush and colour, [for with these he creates] a harmony to the eye, even 
as music does in an instant to the ear. ^ , . 

Quaderni in 7 r. 

[Painting and sculpture] 

Why the picture seen with two eyes will not be an example of such 
relief as the relief seen with two eyes; this is because the picture seen 
with one eye will place itself in relief like the actual relief, having the 
same qualities of light and shade. Quadernim Sr 



Precepts of the Painter 

Tainting is concerned with all the ten attributes 
of sight, namely darkness, brightness, substance 
and colour, form and place, remoteness and 
nearness, movement and rest; and it is with 
these attributes that this my small book will be 

Which is the more difficult: light and shade or good design? 

I maintain that a thing which is confined by a boundary is more 
difficult than one which is free. Shadows have their boundaries at cer- 
tain stages, and when one is ignorant of this his works will be lacking in 
that relief which is the importance and the soul of painting. Design is 
free, in so much as if you see an infinite number of faces they will be all 
different, one with a long nose and one with a short; the painter therefore 
must also assume this liberty, and where there is liberty there is no rule. 

MS. 2038 Bib. Nat. I r. 


The mind of the painter should be like a mirror which always takes 
the colour of the thing that it reflects, and which is filled by as many 
images as there are things placed before it. Knowing therefore that you 
cannot be a good master unless you have a universal power of represent- 
ing by your art all the varieties of the forms which nature produces, — 
which indeed you will not know how to do unless you see them and 
retain them in your mind, — look to it, O Painter, that when you go into 
the fields you give your attention to the various objects, and look care- 
fully in turn first at one thing and then at another, making a bundle of 
different things selected and chosen from among those of less value. 
And do not after the manner of some painters who when tired by 
imaginative work, lay aside their task and take exercise by walking, in 
order to find relaxation, keeping, however, such weariness of mind as 
prevents them either seeing or being conscious of different objects; so 
that often when meeting friends or relatives, and being saluted by them, 
although they may see and hear them they know them no more than 
if they had met only so much air. ^038 Bib. Nat. a r. 

The various contrasts of the different degrees of shadows and lights 
often cause hesitation and confusion to the painter who aspires to imitate 
and reproduce the things that he sees. The reason is that if you see a 
white cloth side by side with a black one, it is certain that the part of this 
white cloth which is next to the black will seem whiter by far than the 
part that is next to something whiter than itself, and the reason of this 
is proved in my Perspective. 



That part of the fold which is farthest from the ends where it is con- 
fined will return most closely to its original form. Everything naturally 
desires to remain in its own state. Drapery being of uniform density and 
thickness on the reverse and on the right side, desires to lie flat* conse- 
quently, whenever any folds or pleats force it to depart from this condition 
of flatness, it obeys the law of this force in that part of itself where it is most 
constrained, and the part farthest away from such constraint you will 
find return most nearly to its original state, that is to say, lying extended 

and full. 

MS. 2038 Bib. Nat. 4 r. 

The body of the atmosphere is full of an infinite number of the 
pyramids composed of radiating straight lines which are caused by the 
boundaries of the surfaces of the bodies in shadow that are found there, 
and the farther they are away from the object which produces them the 
more their angle becomes acute. And although they intersect and inter- 
lace in their passage, nevertheless they do not become confused with each 
other but proceed with divergent course, spreading themselves out and 
becoming diffused through all the surrounding air. 

And they are of equal power among themselves, all equal to each, 
and each equal to all, and by means of them are transmitted the images 
of the objects, and these are transmitted all in all, and all in each part; 
and each pyramid receives of itself in each of its smallest parts the whole 
form of the object which produces it. ms, .0,8 Bib. Nat. 6 v. 


Let the sketches for historical subjects be rapid, and the working of 

the limbs not too much finished. Content yourself with merely giving 

the positions of these limbs, which you will then be able at your leisure 

to finish as you please. o - d-u xt * o 

J T MS. 2038 Bib. Nat. 8 v. 

Among shadows of equal strength that which is nearest to the eye 
will seem of less density . o - d-i. * 

^ MS. 2038 Bib. Nat. 9 V. 

All colours in distant shadows are indistinguishable and undiscernible. 
In the distance all colours are indistinguishable in shadows, because 
an object which is not touched by the principal light has no power to 



Royal Library t Windsor 


transmit its image through the more luminous atmosphere to the eye, 
because the lesser light is conquered by the greater. 

For example, we see in a house that all the colours on the surface of 
the walls are visible instantly and clearly when the windows of the house 
are open; but, if we go out of the house and look through the windows at 
a little distance in order to see the paintings on the walls, we shall see 
instead of them a uniform darkness. 

The painter ought first to exercise his hand by copying drawings by 
good masters; and having acquired facility in this under the advice of 
his instructor, he ought to set himself to copy good reliefs, following the 
rules given below. * 


He who draws from relief ought to take his position so that the eye 
of the figure he is drawing is on a level with his own. And this should 
be done whenever a head has to be drawn from nature, because generally 
figures or people whom you meet in the streets all have their eyes at the 
same level as yours, and if you make them higher or lower you will find 
that your portrait will not resemble them. 


The painter ought always to consider, as regards the wall on which 
he intends to represent a story, the height of the position where he intends 
to place his characters, so that when he makes studies from nature for 
this purpose he should have his eye as much below the thing that he is 
drawing as the said thing appears in the picture above the eye of the 
spectator: otherwise the work will be deserving of censure. 


Painters oftentimes despair of their power to imitate nature, on 
perceiving how their pictures are lacking in the power of relief and vivid- 
ness which objects possess when seen in a mirror, though as they allege 
they have colours that for clearness and depth far surpass the quality of 
the lights and shadows of the object seen in the mirror, arraigning herein 
not reason but their own ignorance, in that they fail to recognise the 
impossibility of a painted object appearing in such relief as to be 


comparable to the objects in the mirror, although both are on a flat surface 
unless they are seen by a single eye. And the reason of this is that when 
two eyes see one thing after another, as in the case oi a b seeing n m, m 
cannot entirely cover n because the base of the visual lines is so broad as 
to cause one to see the second object beyond the first. If however you 
close one eye as r, the object jf will cover up r, because the visual line starts 
in a single point and makes its base in the first object, with the consequence 
that the second being of equal size is never seen. ^ 

Every bodily form as far as concerns the function of the eye is 
divided into three parts, namely substance, shape and colour. The image 
of its substance projects itself farther from its source than its colour or 
its shape; the colour also projects itself farther than the shape, but this 
law does not apply to luminous bodies. 

The above proposition is clearly shown and confirmed by experience, 
for if you see a man near at hand you will be able to recognise the 
character of the substance of the shape and even of the colour, but, if he 
goes some distance away from you, you will no longer be able to recognise 
who he is because his shape will lack character, and if he goes still farther 
away you will not be able to distinguish his colour but he will merely 
seem a dark body, and farther away still he will seem a very small round 
dark body. He will appear round because distance diminishes the various 
parts so much as to leave nothing visible except the greater mass. The 
reason of this is as follows: — We know very well that all the images of 
objects penetrate to the imprensiva^ through a small aperture in the eye; 
therefore if the whole horizon a d enters through a similar aperture and 
the object ^ ^ is a very small part of this horizon, what part must it 
occupy in the minute representation of so great a hemisphere? And 
since luminous bodies have more power in darkness than any others it is 
necessary, since the aperture of the sight is considerably in shadow, as is 
the nature of all holes, that the images of distant objects intermingle 
within the great light of the sky, or if it should be that they remain 
visible they appear dark and black, as every small body must when seen 
in the limpidity of the air. _ ^ 

•i J MS. 2038 Bib. Nat. 12 V. 

\Images in the mr\ 

All bodies together and each of itself fill the surrounding air with an 
^ Imprensiva, see Vol. I, Optics, pp. 237-8. 



infinite number of tbeir images which are all in all this air, and all in the 
parts of it, bearing with them the nature of the body, the colour and the 
form of their cause. 

Perspective is the bridle and rudder of painting. ^ 

Shadows which you see with difficulty, and whose boundaries you 
cannot define — but which you only apprehend and reproduce in your 
work with some hesitation of judgment ~ these you should not represent 
as finished or sharply defined, for the result would be that your work 
would seem wooden. 


Reflections are caused by bodies of a bright nature and of a smooth 
and half-opaque surface, which when struck by the light drive it back 
again to the first object like the rebound of a ball. 


This custom, which is universally adopted by painters for the walls 
of chapels, is by right strongly to be censured, seeing that they repre- 
sent one composition at one level with its landscape and buildings, and 


All solid bodies have their surfaces covered by various degrees of 
light and shadow. The lights are of two kinds: the one is called original 
the other derived. Original I call that which proceeds from the flame of 
the fire, or from the light of the sun, or of the atmosphere. Derived light 
is the light reflected. But, to return to the promised definition, I say that 
there is no luminous reflection on the side of the body which is turned 
towards objects in shadow such as shaded scenes, meadows with grasses 
of varying height, green or bare woods — for these, although the part of 
each branch turned to the original light is imbued with the attributes of 
this light, have nevertheless so many shadows cast by each branch 
separately, and so many shadows cast by one branch on another, that in 
the whole mass there results such a depth of shadow that the light is as 
nothing; hence objects such as these cannot throw any reflected light 
upon bodies opposite to them. ^ ^ 


then mount to the stage above it and make another, and so vary the 
point of sight from that of the first painting, and then make a third, 
and a fourth, in such a way that the work on the one wall shows four 
points of sight, which is extreme folly on the part of such masters. 

Now we know that the point of sight is opposite the eye of the 
spectator of the composition, and if you were to ask me how I should 
represent the life of a saint when it is divided up in several compositions 
on the same wall, to this I reply that you ought to set the foreground 
with its point of sight on a level with the eye of the spectators of the com- 
position, and at this same plane make the chief episode on a large scale, 
and then by diminishing gradually the figures and buildings upon the 
various hills and plains, you should represent all the incidents of the 
story. And on the rest of the wall up to the top you should make trees 
large as compared with the figures, or angels if these are appropriate to 
the story, or birds or clouds or similar things; but otherwise do not put 
yourself to the trouble for the whole of your work will be wrong. 

Figures in relief in the act of movement will in their standing 
position seem naturally to fall forward. 

The youth ought first to learn perspective, then the proportions of 
everything, then he should learn from the hand of a good master in 
order to accustom himself to good limbs; then from nature in order to 
confirm for himself the reasons for what he has learnt; then for a time 
he should study the works of different masters; then make it a habit to 
practise and work at his art. 

How the first picture was nothing but a line which surrounded the 
shadow of a man made by the sun upon a wall. 

How historical pictures ought not to be crowded and confused by 
many figures. 

How old men should be shown with slow listless movements, with 
the legs bent at the knees when they are standing up, with the feet 
parallel and separated one from another, the spine bent low, the head 
leaning forward, and the arms not too far apart. 

How women should be represented in modest attitudes, with legs 
close together, arms folded, and with their heads low and bending side- 

How old women should be represented as bold, with swift passionate 


movements like the infernal furies, and these movements should seem 
quicker in the arms and heads than in the legs. 

Little children should be represented when sitting as twisting them- 
selves about with quick movements, and in shy, timid attitudes when 
standing up. 

How one ought not to give drapery a confusion of many folds, but 
only make them where it is held by the hands or arms, and the rest may 
be sufFered to fall simply where its nature draws it: and do not let the 
contour of the figure be broken by too many lines or interrupted folds. 

How draperies should be drawn from nature: that is, if you wish to 
represent woollen cloth draw the folds from the same material, and if it 
is to be silk, or fine cloth, or homespun, or of linen or crape, show the 
different nature of the folds in each; and do not make a costume as many 
make it upon models covered with pieces of paper or thin leather, for you 
wffl be deceiving yourself greatly. ms. .038 Bib. Nat. 17 v. 


Perspectives are of three kinds. The first has to do with the causes 
of the diminution or as it is called the diminishing perspective of objects 
as they recede from the eye. The second the manner in which colours 
are changed as they recede from the eye. The third and last consists in 
defining in what way objects ought to be less carefuUy finished as they 
are farther away. And the names are these: 

Linear Perspective 
Perspective of Colour 
Vanishing Perspective. 


How figures when dressed in a cloak ought not to show the shape to 
such an extent that the cloak seems to be next to the skin; for surely you 
would not wish that the cloak should be next the skin, since you must 
realise that between the cloak and the skin are other garments which 
prevent the shape of the limbs from being visible and appearing through 
the cloak. And those limbs which you make visible, make thick of their 
kind so that there may seem to be other garments there under the cloak. 
And you should only allow the almost identical thickness of the limbs to 
be visible in a nymph or an angel, for these are represented clad in light 


draperies, which by the blowing of the wind are driven and pressed 
against the various limbs of the figures. 

I N P A I N T I N G 

It is evident that the part of the atmosphere which lies nearest the 
level ground is denser than the rest, and that the higher it rises the lighter 
and more transparent it becomes. 

In the case of large and lofty objects which are some distance away 
from you, their lower parts will not be much seen, because the line by 
which you should see them passes through the thickest and densest 
portion of the atmosphere. But the summits of these heights are seen 
along a line which, although when starting from your eye it is projected 
through the denser atmosphere, yet since it ends at the highest summit 
of the object seen, concludes its course in an atmosphere far more rarefied 
than that of its base. And consequently the farther away from you this 
line extends from point to point the greater is the change in the finer 
quality of the atmosphere. 

Do you, therefore, O painter, when you represent mountains, see 
that from hill to hill the bases are always paler than the summits, and 
the farther away you make them one from another let the bases be paler 
in proportion, and the loftier they are the more they should reveal their 
true shape and colour. „ t,., .. ' 

T MS. 2038 Bib. Nat. 1 8 r. 

How the atmosphere should be represented as paler in proportion 
as you show it extending lower: 

Since the atmosphere is dense near the ground, and the higher it is 
the finer it becomes, therefore when the sun is in the east and you look 
towards the west, taking in a part to the north and to the south, you will 
see that this dense air receives more light from the sun than the finer air, 
because the rays encounter more resistance. And if your view of the 
horizon is bounded by a low plain, that farthest region of the sky will be 
seen through that thicker whiter atmosphere, and this will destroy the 
truth of the colour as seen through such a medium; and the sky will 
seem whiter there than it does overhead, where the line of vision 
traverses a lesser space of atmosphere charged with thick vapours. But 
if you look towards the east the atmosphere will appear darker in pro- 


portion as it is lower, for in this lower atmosphere the luminous rays pass 
less freely. 

How shadows are distributed in different positions, and of the objects 
situated in them: 

If the sun is in the east and you look towards the west you will see 
that all the things which are illuminated are entirely deprived of shadow, 
because what you are looking at is what the sun sees. 

And if you look to the south and the north you will see that all the 
bodies are surrounded by light and shade, because you are looking both 
at the part that does not see and the part that sees the sun. And if you 
look towards the pathway of the sun all the objects will present their 
shaded side to you because this side cannot be seen by the sun. 


Whatever is entirely deprived of light is all darkness. When such is 
the condition of night, if you wish to represent a scene therein, you 
must arrange to introduce a great fire there, and then the things which 
are nearest to the fire will be more deeply tinged with its colour, for 
whatever is nearest to the object partakes most fully of its nature; and 
making the fire of a reddish colour you should represent all the things 
illuminated by it as being also of a ruddy hue, while those which are 
farther away from the fire should be dyed more deeply with the black 
colour of the night. The figures which are between you and the fire 
will appear dark against the brightness of the flame, for that part of the 
object which you perceive is coloured by the darkness of the night, and 
not by the brightness of the fire; those which are at the sides should be 
half in shadow and half in ruddy light; and those visible beyond the edge 
of the flames will all be lit up with ruddy light against a dark back- 
ground. As for their actions, show those who are near it making a 
screen with hands and cloaks as a protection against the unbearable heat, 
with faces turned away as though on the point of flight; while of those 
farther away you should show a great number pressing their hands upon 
their eyes, hurt by the intolerable glare. „s. 203 8 Bib. Nat. 1 8 v. 

Why of two objects of equal size the painted one will look larger 
than that in relief: 

This proposition is not so easy to expound as many others, but I will 
nevertheless attempt to prove it, if not completely then in part. 


Diminishing perspective demonstrates by reason that objects diminish 
in proportion as they are farther away from the eye, and this theory 
is entirely confirmed by experience. Now the lines of sight which are 
between the object and the eye are all intersected at a uniform boundary 
when they reach the surface of the painting; while the lines which pass 
from the eye to the piece of sculpture have different boundaries and are 
of varying lengths. The line which is the longest extends to a limb which 
is farther away than the rest, and consequently this limb appears smaller; 
and there are many lines longer than others, for the reason that there are 
many small parts one farther away than another, and being farther away 
these of necessity appear smaller, and by appearing smaller they effect 
a corresponding decrease in the whole mass of the object. But this does 
not happen in the painting, because as the lines of sight end at the same 
distance it follows that they do not undergo diminution, and as the parts 
are not themselves diminished they do not lessen the whole mass of the 
object, and consequently the diminution is not perceptible in the paint- 

ing as it is in sculpture. 

MS. 2038 Bib. Nat. 19 r. 


When you are representing a white body surrounded by ample 
space, since the white has no colour in itself it is tinged and in part 
transformed by the colour of what is set over against it. If you are look- 
ing at a woman dressed in white in the midst of a landscape the side of 
her that is exposed to the sun will be so dazzling in colour that parts of 
it, like the sun itself, will cause pain to the sight, and as for the side ex- 
posed to the atmosphere — which is luminous because of the rays of the 
sun being interwoven with it and penetrating it — since this atmosphere 
is itself blue, the side of the woman which is exposed to it will appear 
steeped in blue. If the surface of the ground near to her be meadows, 
and the woman be placed between a meadow lit by the sun and the sun 
itself, you will find that all the parts of the folds [of her dress] which are 
turned towards the meadow will be dyed by the reflected rays to the 
colour of the meadow; and thus she becomes changed into the colours 
of the objects near, both those luminous and those non-luminous. 

H 0 W T O R E P R E S E N T T H E L I M B S 
Make muscular such limbs as have to endure fatigue, and those 
which are not so used make without muscles and soft. 



Make figures with such action as may be sufficient to show what the 
figure has in mind 5 otherwise your art will not be worthy of praise. 

MS. 3038 Bib. Nat. 20 r. 


If you have a courtyard which, when you so please, you can cover 
over with a linen awning, the light will then be excellent. Or when you 
wish to paint a portrait, paint it in bad weather, at the fall of the evening, 
placing the sitter with his back to one of the walls of the courtyard. 
Notice in the streets at the fall of the evening when it is bad weather the 
faces of the men and women —what grace and softness they display! 
Therefore, O painter, you should have a courtyard fitted .up with the 
walls tinted in black and with the roof projecting forward a little beyond 
the wall; and the width of it should be ten braccia, and the length twenty 
braccia, and the height ten braccia; and you should cover it over with 
the awning when the sun is on it, or else you should make your portrait 
at the hour of the fall of the evening when it is cloudy or misty, for the 
light then is perfect. 


We see clearly that all the images of the visible things both large and 
small which serve us as objects enter to the sense through the tiny pupil 
of the eye. If, then, through so small an entrance there passes the image 
of the immensity of the sky and of the earth, the face of man — being 
almost nothing amid such vast images of things, because of the distance 
which diminishes it — occupies so little of the pupil as to remain in- 
distinguishable; and having to pass from the outer surface to the seat of 
the sense through a dark medium, that is, through the hollow cells 
which appear dark, this image when not of a strong colour is affected by 
the darkness through which it passes, and on reaching the seat of the 
sense it appears dark. No other reason can be advanced to account for 
the blackness of this point in the pupil; and since it is filled with a 
moisture transparent like the air, it acts like a hole made in a board; 
and when looked into it appears black, and the objects seen in the air, 
whether light or dark, become indistinct in the darkness. 

24s . 



Shadows become lost in the far distance, because the vast expanse of 
luminous atmosphere which lies between the eye and the object seen 
suffuses the shadows of the object with its own colour. 


Diminishing perspective shows us that in proportion as an object is 
farther away the smaller it becomes. And if you look at a man who is at 
the distance of a bowshot away from you and put the eye of a small 
needle close to your eye, you will be able through this to see the images 
of many men transmitted to the eye, and these will all be contained at 
one and the same time within the eye of the said needle. If then the 
image of a man who is distant from you the space of a bowshot is so 
transmitted to your eye as to occupy only a small part of the eye of a 
needle, how should you be able in so small a figure to distinguish or 
discern the nose or mouth or any detail of the body? 

And not seeing these you cannot recognise the man, sincehe does not 
show you the features which cause men to differ in appearance. 


The pit of the throat is above the foot. If an arm be thrown forward 
the pit of the throat moves from above the foot, and if the leg is thrown 
backwards the pit of the throat moves forwards, and so it changes with 
every change of attitude. ^ 


If you wish to represent a tempest properly, consider and set down 
exactly what are the results when the wind blowing over the face of the 
sea and of the land lifts and carries with it everything that is not immov- 
able in the general mass. And in order properly to represent this 
tempest, you must first of all show the clouds, riven and torn, swept 
along in the path of the wind, together with storms of sand blown up 
from the sea shores, and branches and leaves caught up by the irresistible 
fury of the gale and scattered through the air, and with them many other 
things of light weight. The trees and shrubs should be bent to the 
ground, as though showing their desire to follow the direction of the 
wind, with their branches twisted out of their natural growth and their 



leaves tossed and inverted. Of the men who are there, some should have 
fallen and be lying wrapped round by their garments and almost 
indistinguishable on account of the dust, and those, who are left standing 
should be behind some tree with their arms thrown round it to prevent 
the wind from dragging them away; others should be shown crouching 
on the ground, their hands over their eyes because of the dust, their 
garments and hair streaming in the wind. Let the sea be wild and tem- 
pestuous, and between the crests of its waves it should be covered with 
eddying foam, and the wind should carry the finer spray through the 
stormy air after the manner of a thick and all-enveloping mist. 

Of the ships that are there, some you should show with sail rent and 
the shreds of it flapping in the air in company with the broken halyards, 
and some of the masts broken and gone by the board, and the vessel 
itself lying disabled and broken by the fury of the waves, with some of 
the crew shrieking and clinging to the fragments of the wreck. You 
should show the clouds, driven by the impetuous winds, hurled against 
the high mountain tops, and there wreathing and eddying like waves 
that beat upon the rocks; the very air should strike terror through the 
murky darkness occasioned therein by the dust and mist and thick 


When you desire to represent anyone speaking among a group of 
persons you ought to consider first the subject of which he has to treat, 
and how so to order his actions that they may be in keeping with this 
subject. That is, if the subject be persuasive, the actions should serve 
this intention; if it be one that needs to be expounded under various 
heads, the speaker should take a finger of his left hand between two 
fingers of his right, keeping the two smaller ones closed,^ and let his 
face be animated and turned towards the people, with mouth slightly 
opened, so as to give the effect of speaking. And if he is seated let him 
seem to be in the act of raising himself more upright, with his head for- 
ward. And if you represent him standing, make him leaning forward a 
little with head and shoulders towards the populace, whom you should 
show silent and attentive, and all watching the face of the orator with 

^ MS. has serate. M. Ravaisson-Mollien gives searate^ and translates as though 
it were ‘separate’. 

247 , 

^ I 


gestures of admiration. Show the mouths of some of the old men with 
the corners pulled down in astonishment at what they hear, drawing 
back the cheeks in many furrows, with their eyebrows raised where they 
meet, making many wrinkles on their foreheads; and show some sitting 
with the fingers of their hands locked together and clasping their weary 
knees, and others — decrepit old men — with one knee crossed over the 
other, and one hand resting upon it which serves as a cup for the other 
elbow, while the other hand supports the bearded chin. 

MS. 2038 Bib. Nat. 21 r. 

How to heighten the apparent relief in a painting by the use of arti- 
ficial lights and shadows: 

In order to increase the relief in a picture you should make it your 
practice to place between the figure represented and that adjacent object 
which receives its shadow, a line of bright light in order to divide the 
figure from the object in shadow. And in this same object you will make 
two bright parts which shall have between them the shadow cast upon 
the wall by the figure placed opposite: and do this frequently with the 
limbs which you desire should stand out somewhat from their body; and 
especially when the arms cross the breast, show how between the line of 
incidence of the shadow of the arm upon the breast and the real shadow 
of the arm, there remains a streak of light which seems to pass through 
the space that is between the breast and the arm. And the more you wish 
the arm to seem detached from the breast the broader you must make this 
light. And always make it your aim so to arrange bodies against their 
backgrounds that the parts of the bodies that are in shadow end against 
a light background, and the part of the body that is illuminated ends 
against a dark background. 



T ake care that the shadows cast upon the surfaces of bodies by differ- 
ent objects are always undulating with varying curves produced by the 
variety of the limbs that create the shadows and of the object that 
receives the shadow. 


Shadow partakes of the nature of universal things which are all more 
powerful at their beginning and grow weaker towards the end. I refer 
to the beginning of all forms and qualities visible or invisible, and not of 

248 ■ : 


things brought from small beginnings to a mighty growth by time, as a 
great oak would be which has its feeble beginning in a tiny acorn; though 
I would rather say the oak is most powerful at the spot where it is born in 
the ground, for there is the place of its greatest growth. Darkness, there- 
fore, is the first stage of shadow and light is the last. See, therefore, O 
painter, that you make your shadow darkest near to its cause and make 
the end of it become changed into light so that it seems to have no end. 

How the shadows cast by particular lights should be avoided because 
their ends are like their beginnings: 

The shadows cast by the sun or other particular lights do not impart 
grace to the body to which they belong, but rather leave the parts 
separated in a state of confusion with a visible boundary of shadow and 
light. And the shadows have the same strength at the end that they had 
at the beginning. ms. 2038 Bib. Nat. 21 v. 


Shadow is the absence of light*; it is simply the obstruction caused by 
Opaque bodies opposed to luminous rays. Shadow is of the nature of 
darkness, light is of the nature of brightness. The one hides and the 
other reveals. They are always in company attached to the bodies. And 
shadow is more powerful than light for it impedes and altogether de- 
prives objects of brightness, whereas brightness can never altogether 
drive away shadow from bodies, that is from opaque bodies. 

What difference there is between a shadow inseparable from a body 
and a cast shadow: 

An inseparable shadow is one which is never parted from the 
illuminated bodies, as is the case with a ball, for when it is in the light it 
always has one of its sides covered by shadow and this shadow never 
separates from it through any change in the position of the ball. A cast 
shadow may or may not be produced by the body itself. Let us suppose 
the ball to be at a distance of a braccio from the wall and the light to be 
coming from the opposite side: this light will throw just as broad a 
shadow upon the wall as upon the side of the ball that faces the wall. 
Part of a cast shadow will not be visible when the light is below the ball, 
for its shadow will then pass towards the sky and finding there no 



I will not refrain from setting among these precepts a new device for 
consideration which, although it may appear trivial and almost ludicrous, 
is nevertheless of great utility in arousing the mind to various inventions. 

And this is that if you look at any walls spotted with various stains 
or with a mixture of dilferent kinds of stones, if you are about to invent 
some scene you will be able to see in it a resemblance to various different 
landscapes adorned with mountains, rivers, rocks, trees, plains, wide 
valleys and various groups of hills. You will also be able to see divers 
combats and figures in quick movement, and strange expressions of 
faces, and outlandish costumes, and an infinite number of things which 
you can then reduce into separate and well-conceived forms. With 
such walls and blends of different stones it comes about as it does with 
the sound of bells, in whose clanging you may discover every name and 
word that you can imagine. 


Painting is concerned with all the ten attributes of sight, namely 
darkness and brightness, substance and colour, form and place, remoteness 
and nearness, movement and rest; and it is with these attributes that this 
my small book will be interwoven, recalling to the painter by what rules 
and in what way he ought by his art to imitate all things that are 
the work of nature and the adornment of the world. 


As a means of practising this perspective of the variation and loss or 
diminution of the proper essence of colours, take, at distances a hundred 
braccia apart, objects standing in the landscape, such as trees, houses, 
men and places, and in front of the first tree fix a piece of glass so that 
it is quite steady, and then let your eye rest upon it and trace out a tree 
upon the glass above the outline of the tree; and afterwards remove the 
glass so far to one side that the actual tree seems almost to touch the 
one that you have drawn. Then colour your drawing in such a way that 
the two are alike in colour and form, and that if you close one eye both 
seem painted on the glass and the same distance away. Then proceed in 



the same way with a second and a third tree at distances of a hundred 
braccia from each other. And these will always serve as your standards 
and teachers when you are at V'ork on pictures where they can be 
applied, and they will cause the work to be successful in its distance. 

But I find it is a rule that the second is reduced to four-fifths the 
size of the first when it is twenty braccia distant from it. 



Whenever you make a figure of a man or of some graceful animal 
remember to avoid making it seem wooden; that is it should move 
with counterpoise and balance in such a way as not to seem a block 
of wood. 

Those whom you wish to represent as strong should not be shown 
thus except in their manner of turning their heads upon their shoulders. 

MS. 3038 Bib. Nat. 22 V. 


Linear perspective has to do with the function of the lines of sight, 
proving by measurement how much smaller is the second object than 
the first and the third than the second, and so on continually until the 
limit of things seen. I find by experience that if the second object is as 
far distant from the first as the first is from your eye, although as between 
themselves they may be of equal size, the second will seem half as small 
again as the first; and if the third object is equal in size to the second, 
and it is as far beyond the second as the second is from the first, ^ it will 
appear half the size of the second; and thus by successive degrees at 
equal distances the objects will be continually lessened by half, the 
second being half the first — provided that the intervening space does 
not amount to as much as twenty braccia; for at the distance of twenty 
braccia a figure resembling yours will lose four-fifths of its size, and at a 
distance of forty braccia it will lose nine-tenths, and nineteen-twentieths 
at sixty braccia, and so by degrees it will continue to diminish, when the 
plane of the picture is twice your own height away from you, for if the 
distance only equals your own height there is a great difference between 
the first set of braccia and the second. 

^ MS. has ‘third’. 



You should make the figure in the foreground in an historical 
composition proportionately less than life size according to the number 
of braccia that you place it behind the front line, and then make the 
others in proportion to the first by the rule above. 

I give the degrees of the things seen by the eye as the musician 
does of the sounds heard by the ear: 

Although the things seen by the eye seem to touch as they recede 
I will nevertheless found my rule on spaces of twenty braccia, as the 
musician has done with sounds, for although they are united and 
connected together he has nevertheless fixed the degrees from sound to 
sound, calling these first, second, third, fourth and fifth, and so from 
degree to degree he has given names to the varieties of the sound of the 
voice, as it becomes higher or lower. 

A method of making the shadow on figures correspond to their 
light and their shape: 

When you make a figure and wish to see whether the shadow 
corresponds to the light, and is neither redder nor yellower than is the 
nature of the essence of the colour which you wish to show in shadow, 
you should do as follows: with a finger make a shadow upon the illu- 
minated part, and if the accidental shadow made by you is like the 
natural shadow made by your finger upon your work, it will be well then 
by moving the finger nearer or farther off, to make the shadows darker 
or lighter, comparing them constantly with your own. 

MS. 2038 Bib. Nat. 23 r. 


All those objects opposite to the eye which are too near to it will 
have their edges difficult to discern, as happens when objects are near 
to the light and cast a large and indistinct shadow, even so this does when 
it has to judge of objects outside it: in all cases of linear perspective its 
action is similar to that of light. The reason of this is that the eye has 
one principal line [of vision] which dilates as it acquires distance, and 
embraces with exactness of perception large things far away as it does 


small things close at hand. The eye however sends out a multitude of 
lines on either side of this principal centre-line, and these have less power 
to discern correctly as they are farther from the centre in this radiation. 
It follows therefore when an object is placed close to the eye that at that 
stage of nearness to the principal line of vision this is not capable of 
distinguishing the edges of the object, and so these edges must needs 
find themselves amid the lines that have but a poor power of compre- 
hension. Their part in the functions of the eye is like that of setters at 
the chase, who start the prey but cannot catch it. So while they cannot 
themselves apprehend them they are a reason why the principal line of 
vision is diverted to the objects touched by these lines. 

It follows therefore that the objects which have their edges judged 
by these lines are indistinct. 

J MS. 2038 23 V. 


When you wish to know anything well by heart which you have 
studied follow this method:— When you have drawn the same thing so 
many times that it seems that you know it by heart try to do it without 
the model; but have a tracing made of the model upon a thin piece of 
smooth glass and lay this upon the drawing you have made without the 
model. Note well where the tracing and your drawing do not tally, and 
where you find that you have erred bear it in mind in order not to make 
the mistake again. Even return to the model in order to copy the part 
where you were wrong so many times as to fix it in your mind; and if 
you cannot procure smooth glass to make a tracing of the object take a 
piece of very fine parchment well oiled and then dried, and when you 
have used it for one drawing you can wipe this out with a sponge and 
do a second. 


Take a piece of glass of the size of a half sheet of royal folio paper, 
and fix it well in front of your eyes, that is between your eye and the 
object that you wish to portray. Then move away until your eye is two- 
thirds of a braccio away from the piece of glass, and fasten your head by 
means of an instrument in such a way as to prevent any movement of it 
whatsoever. Then close or cover up one eye, and with a brush or a piece 
of red chalk finely ground mark out on the glass what is visible beyond 
it; afterwards copy it by tracing on paper from the glass, then prick it 


out upon paper of a better quality and paint it if you so desire, paying 
careful attention to the aerial perspective. 


If you wish thoroughly to accustom yourself to correct and good 
positions for your figures, fasten a frame or loom divided into squares 
by threads between your eye and the nude figure which you are 
representing, and then make the same squares upon the paper where 
you wish to draw the said nude but very faintly. You should then 
place a pellet of wax on a part of the network to serve as a mark which 
as you look at your model should always cover the pit of the throat, or if 
he should have turned his back make it cover one of the vertebrae of the 
neck. And these threads will instruct you as to all the parts of the body 
which in each attitude are found below the pit of the throat, below the 
angles of the shoulders, below the breasts, the hips and the other parts 
of the body; and the transverse lines of the network will show you how 
much higher the figure is above the leg on which it is posed than above 
the other, and the same with the hips, the knees and the feet. But always 
fix the net by a perpendicular line and then see that all the divisions that 
you see the nude take in the network, the nude that you draw takes in 
the network of your sketch. The squares you draw may be as much 
smaller than those of the network in proportion as you wish your figure 
to be less than life size: then keep in mind in the figures that you make, 
the rule of the corresponding proportions of the limbs as the network 
has revealed it to you, and this should be three and a half braccia in 
height and three wide, at a distance of seven braccia from you and one 
from the nude figure. 

MS. 2038 Bib. Nat. 24 r. 


When you wish to see whether the general effect of your picture 

corresponds with that of the object represented after nature, take a 
mirror and set it so that it reflects the actual thing, and then compare 
the reflection with your picture, and consider carefully whether the 
subject of the two images is in conformity with both, studying especially 
the mirror. The mirror ought to be taken as a guide ■— that is, the flat 
mirror — for within its surface substances have many points of 
resemblance to a picture; namely, that you see the picture made upon one 
plane showing things which appear in relief, and the mirror upon one 



plane does the same. The picture is one single surface, and the mirror 
is the same. 

The picture is intangible, inasmuch as what appears round and 
detached cannot be enclosed within the hands, and the mirror is the 
same. The mirror and the picture present the images of things sur- 
rounded by shadow and light, and each alike seems to project con- 
siderably from the plane of its surface. And since you know that the 
mirror presents detached things to you by means of outlines and shadows 
and lights, and since you have moreover amongst your colours more 
powerful shadows and lights than those of the mirror, it is certain that if 
you but know well how to compose your picture it will also seem a 
natural thing seen in a great mirror. ^ 

Of the poor excuse made by those who falsely and unworthily get 
themselves styled painters: 

There is a certain class of painters who though they have given but 
little attention to study claim to live in all the beauty of gold and azure. 
These aver — such is their folly! — that they are not able to work up 
to their best standard because of the poor payment, but that they have 
the knowledge and could do as well as any other if they were well paid. 

But see now the foolish folk! They have not the sense to keep by 
them some specimen of their good work so that they may say, ‘this is at 
a high price, and that is at a moderate price and that is quite cheap’, and 
so show that they have work at all prices. 3;^ ^ 


There is another kind of perspective which I call aerial, because by 
the difference in the atmosphere one is able to distinguish the various 
distances of different buildings when their bases appear to end on a 
single line, for this would be the appearance presented by a group of 
buildings on the far side of a wall, all of which as seen above the top of 
the wall look to be the same size; and if in painting you wish to make one 
seem farther away than another you must make the atmosphere some- 
what heavy. You know that in an atmosphere of uniform density the 
most distant things seen through it, such as the mountains, in conse- 
quence of the great quantity of atmosphere which is between your eye 
and them, will appear blue, almost of the same colour as the atmosphere 
when the sun is in the east. Therefore you should make the building 

. '^55 ' .. 


which is nearest above the wall of its natural colour, and that which is 
more distant make less defined and bluer; and one which you wish 
should seem as far away again make of double the depth of blue, and 
one you desire should seem five times as far away make five times as 
blue. And as a consequence of this rule it will come about that the 
buildings which above a given line appear to be of the same size will be 
plainly distinguished as to which are the more distant and which larger 
than the others. 


We may frankly admit that certain people deceive themselves who 
apply the title ‘a good master’ to a painter who can only do the head or 
the figure well. Surely it is no great achievement if by studying one 
thing only during his whole lifetime he attain to some degree of 
excellence therein! But since, as we know, painting embraces and con- 
tains within itself all the things which nature produces or which result 
from the fortuitous actions of men, and in short whatever can be compre- 
hended by the eyes, it would seem to me that he is but a poor master 
who makes only a single figure well. 

For do you not see how many and how varied are the actions which 
are performed by men alone.? Do you not see how many different kinds 
of animals there are, and also of trees and plants and flowers? What 
variety of hilly and level places, of springs, rivers, cities, public and 
private buildings; of instruments fitted for man’s use; of divers costumes, 
ornaments and arts? — Things which should be rendered with equal 
facility and grace by whoever you wish to call a good painter. 


Which is better — to draw from nature or from the antique? 

And which is more difficult —the lines or the light and shade? 

MS. 2038 Bib. Nat. 25 V, 



I have proved in my own case that it is of no small benefit on finding 
oneself in bed in the dark to go over again in the imagination the 
main outlines of the forms previously studied, or of other noteworthy 



things conceived by ingenious speculation; and this exercise is entirely 
to be commended, and it is useful in fixing things in the memory. 

How the painter ought to be desirous of hearing every man’s 

opinion as to the progress of his work: 

Surely when a man is painting a picture he ought not to refuse to 
hear any man’s opinion, for we know very well that though a man may 
not be a painter he may have a true conception of the form of another 
man, and can judge aright whether he is hump-backed or has one 
shoifider high or low, or whether he has a large mouth or nose or other 

Since then we recognise that men are able to form a true judgment 
as to the works of nature, how much the more does it behove us to admit 
that they are able to judge our faults. For you know hovv much a man 
is deceived in his own works, and if you do not recognise this in your own 
case observe it in others and then you will profit by their mistakes. 
Therefore you should be desirous of hearing patiently the opimons of 
others, and consider and reflect carefully whether or no he who censures 
you has reason for his censure; and correct your work if you find that 
he is right, but if not, then let it seem that you have not understood 
him, or, in case he is a man whom you esteem, show him by argument 
why it is that he is mistaken. 

How in works of importance a man should not trust so entirely to 

his memory as to disdain to draw from nature: ^ _ 

Any master who let it be understood that he could himself recall all 
the forms and effects of nature would certainly appear to me to be 
endowed with great ignorance, considering that these effects are 
infinite and that our memory is not of so great capaaty as to suffice 

Do you therefore, O painter, take care lest the greed for gain prove 
a stronger incentive than renown in art, for to gain this renown is a 
far greater thing than is the renown of riches. _ , , j 

For these, then, and other reasons which might be given, you should 
apply yourself first of all to drawing, in order to present to the eye in 
vifible form the purpose and invention created originally in your 
imagination; then proceed to take from it or add to it until you saUsfy 
yourself; then have men arranged as models draped or nude in the way 


in which you have disposed them in your work; and make the pro- 
portions and size in accordance with perspective, so that no part of the 
work remains that is not so counselled by reason and by the effects in 

And this will be the way to make yourself renowned in your art. 

An object which is represented in white and black will appear in 
more pronounced relief than any other: and therefore I would remind 
you, O painter, that you should clothe your figures in as bright colours 
as you can, for if you make them dark in colour they will be only in 
slight relief and be very little visible at a distance. This is because the 
shadows of all objects are dark, and if you make a garment dark there 
will be only a slight difference between its lights and shades, whereas 
with the bright colours there are many grades of difference. 

MS. 2038 Bib. Nat 26 r. 

A F A C E 

If you desire to acquire facility in keeping in your mind the 
expression of a face, first learn by heart the various different kinds of 
heads, eyes, noses, mouths, chins, throats, and also necks and shoulders. 
Take as an instance noses: — they are of ten types: straight, bulbous, 
hollow, prominent either above or below the centre, aquiline, regular, 
simian, round, and pointed. These divisions hold good as regards 
profile. Seen from in front, noses are of twelve types: thick in the middle, 
thin in the middle, with the tip broad, and narrow at the base, and narrow 
at the tip, and broad at the base, with nostrils broad or narrow, or high 
or low, and with the openings either visible or hidden by the tip. 
And similarly you will find variety in the other features; of which things 
you ought to make studies from nature and so fix them in your mind. 
Or when you have to draw a face from memory, carry with you a small 
note-book in which you have noted down such features, and then when 
you have cast a glance at the face of the person whom you wish to draw 
you can look privately and see which nose or mouth has a resemblance 
to it, and make a tiny mark against it in order to recognise it again at 
home. Of abnormal faces I here say nothing, for they are kept in mind 
without difficulty. 


precepts of the painter 


When you, draughtsmen, wish to find some profitable recreation in 
games you should always practise things which may be of use in your 
profession, that is by giving your eye accuracy of judgment so that it 
may know how to estimate the truth as to the length and breadth ot 
objects. So in order to accustom the mind to such things let one of you 
a straight line anywhere on a wall; and then let each of you take a 
light rush or straw in his hand, and let each cut his own to the length 
which the first line appears to him when he is distant from it a space or 
ten braccia, and then let each go up to the copy in order to measure it 
against the length which he has judged it to be, and he whose measure 
comes nearest to the length of the copy has done best and is the winner, 
and he should receive from all the prize which was previously agreed 
pon by you. Furthermore you should take measurements fore- 
shortened, that is, you should take a spear or some other stick and loo 
before you to a certain point of distance, and then let each set himself to 
reckon how many times this measure is contained in the said distance. 
Another thing is to see who can draw the best line one braccio in length, 
and this may be tested by tightly drawn thread. ; 

Diversions such as these enable the eye to acquire accuracy ot 
judgment, and this is the primary essential of painting. 


O R N O 

I say and am prepared to prove that it is much better to be in the 
company of others when you draw rather than alone, for many reasons. 
The first is that you will be ashamed of being seen m the raiis of the 
draughtsmen if you are outclassed by them, and this feehng of shame twll 
cause you to make progress in study; secondly a rather commendable 
will stimulate you to join the number of those who are mor 
than you are, for the praises of the others will serve you as a 
spur; yet another is that you will acquire something 
anyone whose work is better than yours, while if you are better than th 
others you will profit by seeing howto avoid their errors, and the praises 

of others will tend to increase your powers. ms. 2038 Bib, Nat. 26 v. 



The winter evenings should be spent by youthful students in study 
of the things prepared during the summer; that is, all the drawings from 
the nude which you have made in the summer should be brought 
together, and you should make a choice from among them of the best 
limbs and bodies, and practise at these and learn them by heart. 

O F A T T I T U D E S 

Afterwards in the ensuing summer you should make choice of some 
one who has a good presence, and has not been brought up to wear 
doublets, and whose figure consequently has not lost its natural bearing, 
and make him go through various graceful and elegant movements. 
If he fails to show the muscles very clearly within the outlines of the 
limbs, this is of no consequence. It is enough for you merely to obtain 
good attitudes from the figure, and you can correct the limbs by those 
which you have studied during the winter. 


The painter who has acquired a knowledge of the nature of the 
sinews, muscles, and tendons will know exactly in the movement of any 
limb how many and which of the sinews are the cause of it, and which 
muscle by its swelling is the cause of this sinew’s contracting, and which 
sinews having been changed into most delicate cartilage surround and 
contain the said muscle. So he will be able in divers ways and uni- 
versally to indicate the various muscles by means of the different 
attitudes of his figures; and he will not do like many who in different 
actions always make the same things appear in the arm, the back, the 
breast, and the legs; for such things as these ought not to rank in the 
category of minor faults. 


Methinks it is no small grace in a painter to be able to give a pleasing 
air to his figures, and whoever is not naturally possessed of this grace 
may acquire it by study, as opportunity offers, in the following manner. 
Be on the watch to take the best parts of many beautiful faces of which 
the beauty is established rather by general repute than by your own 
■ : 360. 

Royal Library, Windsor 


judgment, for you may readily deceive yourself by selecting such faces 
as bear a resemblance to your own, since it would often seem that such 
similarities please us; and if you were ugly you would not select beautiful 
faces, but would be creating ugly faces like many painters whose 
types often resemble their master; so therefore choose the beautiful ones 
as I have said, and fix them in your mind. „ 

MS, 2038 Bib, Nat. 27 r, 


The painter or draughtsman ought to be solitary, in order that the 
well-being of the body may not sap the vigour of the mind; and more 
especially when he is occupied with the consideration and investigation 
of things which by being continually present before his eyes furnish 
food to be treasured up in the memory^ 

If you are alone you belong entirely to yourself; if you are accom- 
panied even by one companion you belong only half to yourself, or 
even less in proportion to the thoughtlessness of his conduct; and if you 
have more than one companion you will fall more deeply into the same 

If you should say, T will take my own course; I will retire apart, so 
that I may be the better able to investigate the forms of natural objects’, 
then I say this must needs turn out badly, for you will not be able to 
prevent yourself from often lending an ear to their chatter; and not being 
able to serve two masters you will discharge badly the duty of com- 
panionship, and even worse that of endeavouring to realise your con- 
ceptions in art. 

But suppose you say, T will withdraw so far apart that their words 
shall not reach me nor in any way disturb me’. I reply that in this case 
you will be looked upon as mad, and bear in mind that in so doing you 
will then be solitary. 

If you must have companionship choose it from your studio; it may 
then help you to obtain the advantages which result from different 
methods of study. All other companionship may prove extremely 
harmful. „ , , 

MS. 2038 Bib. Nat. 27 V, and r. 

Of the method of learning aright how to compose groups of figures 
in historical pictures: 

When you have thoroughly learnt perspective, and have fixed in 
your memory all the various parts and forms of things, you should often 

■ 261 


amuse yourself when you take a walk for recreation, in watching and 
taking note of the attitudes and actions of men as they talk and dispute, 
or laugh or come to blows one with another, both their actions and those 
of the bystanders who either intervene or stand looking on at these 
things; noting these down with rapid strokes in this way, ^ in a little 
pocket-book, which you ought always to carry with you. And let this 
be of tinted paper, so that it may not be rubbed out; but you should 
change the old for a new one, for these are not things to be rubbed out 
but preserved with the utmost diligence; for there is such an infinite 
number of forms and actions of things that the memory is incapable of 
preserving them, and therefore you should keep those [sketches] as your 
patterns and teachers. 



If as draughtsman you wish to study well and profitably, accustom 
yourself when you are drawing to work slowly, and to determine between 
the various lights, which possess the highest degree and measure of 
brightness, and similarly as to the shadows, which are those that are 
darker than the rest, and in what manner they mingle together, and to 
compare their dimensions one with another; and so with the contours to 
observe which way they are tending, and as to the lines what part of 
each is curved in one way or another, and where they are more or less 
conspicuous and consequently thick or fine; and lastly to see that your 
shadows and lights may blend without strokes or lines in the manner of 
smoke. And when you shall have trained your hand and judgment with 
this degree of care it will speedily come to pass that you will have no 
need to take thought thereto. „ 

° MS. 2038 Bib. Nat. 27 V. 


We know well that mistakes are more easily detected in the works of 
Others than in one’s own, and that oftentimes while censuring the small 
faults of others you will overlook your own great faults. In order to 
avoid such ignorance make yourself first of all a master of perspective, then 
gain a complete knowledge of the proportions of man and other animals, 
and also make yourself a good architect, that is in so far as concerns the 
form of the buildings and of the other things which are upon the earth, 
^ Sketch of figure in text of MS. 

• ■ 262 


which are infinite in form; and the more knowledge you have of these 
the more will your work be worthy of praise; and for those things in 
which you have no practice do not disdain to draw from nature. But 
to return to what has been promised above, I say that when you are 
painting you should take a flat mirror and often look at your work 
within it, and it will then be seen in reverse, and will appear to be by 
the hand of some other master, and you will be better able to judge of 
its faults than in any other way. 

It is also a good plan every now and then to go away and have a 
little relaxation; for then when you come back to the work your 
judgment will be surer, since to remain constantly at work will cause 
you to lose the power of judgment. 

It is also advisable to go some distance away, because then the work 
appears smaller, and more of it is taken in at a glance, and a lack of 
harmony or proportion in the various parts and in the colours of the 
objects is more readily seen. . 

W H O P A I N T 

We know clearly that the sight is one of the swiftest actions that can 
exist, for in the same instant it surveys an infinite number of forms; 
nevertheless it can only comprehend one thing at a time. To take an 
instance: you, O Reader, might at a glance look at the whole of this 
written page, and you would instantly decide that it is full of various 
letters, but you will not recognise in this space of time either what 
letters they are or what they purport to say, and therefore it is necessary 
for you if you wish to gain a knowledge of these letters to take them 
word by word and line by line. 

Again, if you wish to go up to the summit of a building it will be 
necessary for you to ascend step by step, otherwise it will be impossible 
to reach the top. So I say to you whom nature inclines to this art that 
if you would have a true knowledge of the forms of different objects 
you should commence with their details, and not pass on to the second 
until the first is well in your memory and you have practised it. If you 
do otherwise you will be throwing away time, and to a certainty you 
will greatly prolong the period of study. And remember to acquire 
dUigence rather than facihty. ^ 



Further I remind you to pay great attention in giving limbs to your 
figures, so that they may not merely appear to harmonize with the size 
of the body but also with its age. So the limbs of youths should have 
few muscles and veins, and have a soft surface and be rounded and 
pleasing in colour; in men they should be sinewy and full of muscles; 
in old men the surface should be wrinkled, and rough, and covered with 
veins, and with the sinews greatly protruding. 

How little children have their joints the reverse of those of men in 
their thickness: 

Little children have all the joints slender while the intervening parts 
are thick; and this is due to the fact that the joints are only covered by 
skin and there is no flesh at all over them, and this skin acts as a sinew 

to gird and bind together the bones; and a flabby layer of flesh is found 
between one joint and the next, shut in between the skin and the bone. 
But because the bones are thicker at the joints than between them, the flesh 
as the man grows up loses that superfluity which existed between the 
skin and the bone, and so the skin is drawn nearer to the bone and causes 
the limbs to seem more slender. But since there is nothing above the 
joints except cartilaginous and sinewy skin, this cannot dry up, and not 
being dried up it does not shrink. So for these reasons the limbs of 
children are slender at the joints and thick between the joints, as is seen 
in the joints of the fingers, arms, and shoulders which are slender and 
have great dimples; and a man on the contrary has all the joints of 
fingers, arms, and legs thick, and where children have hollows men have 
the joints protruding. 

B O Y S A N D M E N 

I find a great difference between men and small boys in the length 
from one joint to another; for whereas the distance from the joint of the 
shoulder to the elbow, and from the elbow to the tip of the thumb, 
and, from the humerus of one of the shoulders to the other, in a man 
is twice the head, in a child it is only once, because nature fashions 
the stature of the seat of the intellect for us before that of its active 


Make first a general shadow over the whole of the extended part 
which does not see the light; then give to it the half shadows and the 
strong shadows, contrasting these one with another. 

And similarly give the extended light in half-^tone, adding after- 
wards the half-lights and the high lights and contrasting these in the 

same manner. 

MS. 2038 Bib. Nat. 28 v. 

In what way you ought to make a head so that its parts may fit into 
their true positions: 

To make a head so that its features are in agreement with those of a 
head that turns and bends, use these means: you know that the eyes, 
eyebrows, nostrils, corners of the mouth and sides of the chin, jaw, cheeks, 
ears and all the parts of a face are placed at regular positions upon the 
face, therefore when you have made the face, make lines which pass 
from one corner of the eye to the other; and so also for the position of 
each feature. Then having continued the ends of these lines beyond the 
two sides of the face, observe whether on the right and the left the spaces 
in the same parallel are equal. But I would specially remind you that 
you must make these lines extend to the point of your vision. 

The way to represent the eighteen actions of man: [these are] rest, 
movement, speed ; erect, leaning, seated, bending, kneeling, lying down, 
suspended; carrying, being carried, pushing, dragging, striking, being 
struck, pressing down and raising up. 

You will treat first of the lights cast by windows to which you will 
give the name of restricted light; then treat of the lights of landscape to 
which you will give the name of free light; then treat of the light of 
luminous bodies. 


You know that you cannot make any animal without it having its 
limbs such that each bears some resemblance to that of some one of the 
other animals. If therefore you wish to make one of your imaginary 
animals appear natural — let us suppose it to be a dragon — take for its 
head that of a mastiff or setter, for its eyes those of a cat, for its ears 
■ ■ 265,, 


those of a porcupine, for its nose that of a greyhound, with the eyebrows 
of a lion, the temples of an old cock and the neck of a water-tortoise. 


See that when you are drawing and make a beginning of a line, that 
you look over all the object that you are drawing for any detail whatever 
which lies in the direction of the line that you have begun. 

MS. 2038 Bib. Nat. 29 r. 

How a figure is not worthy of praise unless such action appears in it 
as serves to express the passion of the soul: 

That figure is most worthy of praise which by its action best expresses 
the passion which animates it. 


An angry figure should be represented seizing someone by the hair 
and twisting his head down to the ground, with one knee on his ribs, 
and with the right arm and fist raised high up; let him have his hair 
dishevelled, his eyebrows low and knit together, his teeth clenched, the 
two corners of his mouth arched, and the neck which is all swollen and 
extended as he bends over the foe, should be full of furrows. 


A man who is in despair you should make turning his knife against 
himself, and rending his garments with his hands, and one of his hands 
should be in the act of tearing open his wound. Make him with his 
feet apart, his legs somewhat bent, and the whole body likewise bending 
to the ground, and with his hair torn and streaming. 


The limbs should fit the body gracefully in harmony with the effect 
you wish the figure to produce; and if you desire to create a figure which 
shall possess a charm of its own, you should make it with limbs graceful 
and extended, without showing too many of the muscles, and the few 
which your purpose requires you to show indicate briefly, that is without 
giving them prominence, and with the shadows not sharply defined, and 
the limbs, and especially the arms, should be easy, that is that no limb 
should be in a straight line with the part that adjoins it. And if the hips 
which form as it were the poles of the man, are by his position placed 

266 ■ 


so that the right is higher than the left, you should make the top shoulder- 
joint so that a line drawn from it perpendicularly falls on the most 
prominent part of the hip, and let this right shoulder be lower than the 

And let the hollow of the throat always be exactly over the middle 
of the joint of the foot which is resting on the ground. The leg which 
does not support the weight should have its knee' below the other and 
near to the other leg. 

The positions of the head and arms are numberless, and therefore I 
will not attempt to give any rule; it will suffice that they should be 
natural and pleasing and should bend and turn in various ways, with the 
joints moving freely so that they may not seem like pieces of wood. 


If as experience shows luminous rays come from a single point, and 
proceed in the form of a sphere from this point radiating and spreading 
themselves through the air, the farther they go the more they are 
dispersed; and an object placed between the light and the wall is always 
reproduced larger in its shadow, because the rays that strike it have 
become larger by the time they have reached the wall. 

MS. 2038 Bib. Nat. 29 v. 


As regards the arrangement of the limbs, you should bear in mind 
that when you wish to represent one who by some chance has either to 
turn backwards or on one side, you must not make him move his feet 
and all his limbs in the same direction as he turns his head ; but you 
should show the process spreading itself and taking effect over the four 
sets of joints, namely those of the foot, the knee, the hip, and the neck. 
And if you let his weight rest on the right leg, you should make the 
knee of the left bend inwards; and the foot of it should be slightly raised 
on the outside, and the left shoulder should be somewhat lower than 
the right; and the nape of the neck should be exactly above the outer 
curve of the ankle of the left foot, and the left shoulder should be above 
the toe of the right foot in a perpendicular line. And always so dispose 
your figures that the direction in which the head is turned is not that in 
which the breast faces, since nature has for our convenience so formed 

267- ■■ 


the neck that it can easily serve the different occasions on which the eye 
desires to turn in various directions; and to this same organ the other 
joints are in part responsive. And if ever you show a man sitting with 
his hands at work upon something by his side, make the chest turn upon 
the hip joints. 


A body which finds itself placed between two equal lights will put 
forth two shadows, which will take their direction equally according to 
the lines of the two lights. And if you move the body farther away or 
bring it nearer to one of the lights, the shadow which points to the nearer 
light will be less deep than that which points to the one more remote. 


If an object placed in front of a particular light be very near to it 
you will see it cast a very large shadow on the opposite wall, and the 
farther you remove the object from the light the smaller will the shadow 



C A U S E W I L L B E O U T O F P R O P 0 R T I O N 
The want of proportion of the shadow which is greater than its 
cause, arises from the fact that as the light is less than its object it cannot 
be at an equal distance from the extremities of the object, and the part 
which is at a greater distance increases more than those which are nearer, 
and therefore the shadow increases. 

Atmosphere which surrounds a light almost partakes of the nature 
of this light in brightness and in warmth; the farther away it recedes 
the more it loses this resemblance. An object which casts a large shadow 
is near to the light and finds itself lit up both by the light and by the 
luminous atmosphere, and consequently this atmosphere leaves the 
contours of the shadow indistinct. „ 

MS. 2038 Bib. Nat. 30 r. 

Rojal Uhrary, Windsor 



Show first the smoke of the artillery mingled in the air with the dust 
stirred up by the movement of the horses and of the combatants. This 
process you should express as follows: the dust, since it is made up of 
earth and has weight, although by reason of its fineness it may easily 
rise and mingle with the air, will nevertheless readily fall down again, 
and the greatest height will be attained by such part of it as is the finest, 
and this will in consequence be the least visible and will seem almost the 
colour of the air itself. 

The smoke which is mingled with the dust-laden air will as it rises 
to a certain height have more and more the appearance of a dark cloud, 
at the summit of which the smoke will be more distinctly visible than 
the dust. The smoke will assume a bluish tinge, and the dust will keep 
its natural colour. From the side whence the light comes this mixture of 
air and smoke and dust will seem far brighter than on the opposite side. 

As for the combatants the more they are in the midst of this turmoil 
the less they will be visible, and the less will be the contrast between 
their lights and shadows. 

You should give a ruddy glow to the faces and the figures and the 
air around them, and to the gunners and those near to them, and this 
glow should grow fainter as it is farther away from its cause. The 
figures which are between you and the light, if far away, will appear 
dark against a light background, and the nearer their limbs are to the 
ground the less will they be visible, for there the dust is greater and 
thicker. And if you make horses galloping away from the throng, make 
little clouds of dust as far distant one from another as is the space between 
the strides made by the horse, and that cloud which is farthest away from 
the horse should be the least visible, for it should be high and spread out 
and thin, while that which is nearest should be most conspicuous and 
smallest and most compact. 

Let the air be full of arrows going in various directions, some 
mounting upwards, others falling, others flying horizontally; and let the 
balls shot from the guns have a train of smoke following their course. 
Show the figures in the foreground covered with dust on their hair and 
eyebrows and such other level parts as afford the dust a space to lodge. 

Make the conquerors running, with their hair and other light things 
streaming in the wind, and with brows bent down; and they should be 
thrusting forward opposite limbs, that is, if a man advances the right 

269 ' 


foot, the left arm should also come forward. If you represent anyone 
fallen you should show the mark where he has been dragged through 
the dust which has become changed to blood-stained mire, and round 
about in the half-liquid earth you should show the marks of the 
trampling of men and horses who have passed over it. 

Make a horse dragging the dead body of his master, and leaving 
behind him in the dust and mud the track of where the body was 
dragged along. 

Make the beaten and conquered pallid, with brows raised and knit 
together, and let the skin above the brows be all full of lines of pain; at 
the sides of the nose show the furrows going in an arch from the nostrils 
and ending where the eye begins, and show the dilatation of the nostrils 
which is the cause of these lines; and let the lips be arched displaying 
the upper row of teeth, and let the teeth be parted after the manner of 
such as cry in lamentation. Show someone using his hand as a shield 
for his terrified eyes, turning the palm of it towards the enemy, and 
having the other resting on the ground to support the weight of his 
body; let others be crying out with their mouths wide open, and fleeing 
away. Put all sorts of armour lying between the feet of the combatants, 
such as broken shields, lances, swords, and other things like these. 
Make the dead, some half-buried in dust, others with the dust all mingled 
with the oozing blood and changing into crimson mud; and let the line 
of the blood be discerned by its colour, flowing in a sinuous stream from 
the corpse to the dust. Show others in the death agony grinding their 
teeth and rolling their eyes, with clenched fists grinding against their 
bodies and with legs distorted. Then you might show one, disarmed 
and struck down by the enemy, turning on him with teeth and nails to 
take fierce and inhuman vengeance; and let a riderless horse be seen 
galloping with mane streaming in the wind, charging among the enemy 
and doing them great mischief with his hoofs. 

You may see there one of the combatants, maimed and fallen on the 
ground, protecting himself with his shield, and the enemy bending down 
over him and striving to give him the fatal stroke; there might also be 
seen many men fallen in a heap on top of a dead horse ; and you should 
show some of the victors leaving the combat and retiring apart from 
the crowd, and with both hands wiping away from eyes and cheeks the 
thick layer of mud caused by the smarting of their eyes from the dust.^ 
^ MS. has per lamor della polvere. 


And the squadrons of the reserves should be seen standing full of 
hope but cautious, with eyebrows raised, and shading their eyes with 
their hands, peering into the thick, heavy mist in readiness for the 
commands of their captain; and so too the captain with his staff raised, 
hurrying to the reserves and pointing out to them the quarter of the 
field where they are needed; and you should show a river, within which 
horses are galloping, stirring the water all around with a heaving mass of 
waves and foam and broken water, leaping high into the air and over the 
legs and bodies of the horses; but see that you make no level spot of 
ground that is not trampled over with blood. 

MS. 2038 Bib. Nat. 31 r. and 30 V. 


This point ought to be at the same level as the eye of an ordinary 
man; and the end of the flat country which borders upon the sky should 
be made of the same height as the line where the earth touches the horizon, 
except for the mountains which are in liberty. „ 

•' MS. 2038 Bib. Nat. 31 r. 

^ ^ ^ ^ B ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 

I say that when objects appear of minute size, it is due to the said 
objects being at a distance from the eye; and when this is the case, there 
must of necessity be a considerable quantity of atmosphere between the 
eye and the object, and this atmosphere interferes with the distinctness 
of the form of the objects, and consequently the minute details of these 
bodies will become indistinguishable and unrecognisable. 

Therefore, O painter, you should make your lesser figures only 
suggested, and not highly finished; for if you do otherwise, you will 
produce effects contrary to those of nature, your mistress. 

The object is small because of the great space which exists between 
the eye and it. This great space contains within itself a great quantity 
of atmosphere; and this atmosphere forms of itself a dense body which 
interposes and shuts out from the eye the minute details of the objects. 


Since one sees by experience that all bodies are surrounded by 
shadow and light it is expedient, O painter, that you so dispose the part 



illuminated that it is outlined against a dark object, and that in the same 
wav the part of the body in shadow is outlined against a bright object. 
And this rule will be a great help to you in giving relief to your figures. 

o F D R A W I N G . 

When you have to draw from nature stand three times as far away 

as the size of the object that you are drawing.^ 

Why does a painting seem better in a mirror than outside it. 


This benign nature so provides that over all the world you nnd 
something to imitate. 


Where the shadow is bounded by light, note carefully where it is 
lighter or darker, and where it is more or less indistinct towards the 
light; and above all I would remind you that in youthful figures you 
should not make the shadows end like stone, for the flesh retains a slight 
transparency, as may be observed by looking at a hand held between the 
eye and the sun, when it is seen to flush red and to be of a luminous 

transparency. _ i. r -u^ 

And let the part which is brightest in colour be between the lights 

and the shadows. And if you wish to see what depth of shadow is needed 
for the flesh, cast a shadow over it with your finger, and according as you 
wish it to be lighter or darker, hold your finger nearer or farther away 
from the picture, and then copy this shadow. 


Those trees and shrubs which are more split up into a quantity of 
thin branches ought to have less density of shadow. The trees and the 
shrubs which have larger leaves cast a greater shadow. 

MS. 2038 Bib. Nat. 31 V. 


The disposition of the light should be in harmony with the natural 
conditions under which you represent your figure; that is, if you are 
representing it in sunlight, make the shadows dark with great spaces of 
light, and mark the shadows of all the surrounding bodies and their 

. . , 


shadows upon the ground. If you represent it in dull weather^s make 
only a slight difference between the hghts and the shadows, and do not 
make any other shadow at the feet. If you represent it within doors, 
make a strong difference between the lights and shadows and show the 
shadow on the ground, and if you represent a window covered by a 
curtain and the wall white there should be little difference between the 
lights and shadows. If it is lit by a fire you should make the lights ruddy 
and powerful and the shadows dark; and the shadows should be sharply 
defined where they strike the walls or the floor, and the farther away they 
extend from the body the broader and larger should they become. And 
if it be lit in part by the fire and in part by the atmosphere, make the 
part lit by the atmosphere the stronger, and let that lit by the fire be 
almost as red as fire itself. And above all let the figures that you paint 
have sufficient light and from above, that is all living persons whom you 
paint, for the people whom you see in the streets are all lighted from 
above; and I would have you know that you have no acquaintance so 
intimate but that if the light fell on him from below you would find it 
difficult to recognise him. 

T H E 0 R D E R O F L E A R N I N G T O D R A W 

First of all copy drawings by a good master made by his art from 
nature and not as exercises; then from a relief, keeping by you a drawing 
done from the same relief; then from a good model; and of this you 
ought to make a practice. 

T O D R A W F R O M N A T U R E 

When you are drawing from nature the light should be from the 
north, so that it may not vary; and if it is from the south keep the window 
covered with a curtain so that though the sun shine upon it all day long 
the light will undergo no change. The elevation of the light should be 
such that each body casts a shadow on the ground which is of the same 
length as its height. 


Since we see that the quality of colours becomes known by means of 
light, it is to be inferred that where there is most light there the true 

'S 2 , ■ ■ ' . . 273 . 


quality of the colour so illuminated will be most visible, and where there 
is most shadow there the colour will be most affected by the colour of 
the shadow. Therefore, O painter, be mindful to show the true quality 
of the colours in the parts which are in light. 


Each part of the surface of a body is in part affected by the colour 
of the thing opposite to it. 


If you set a spherical body in the midst of different objects, that is, 
so that on the one side it has the light of the sun and on the side opposite 
there is a wall illuminated by the sun, which may be green or some other 
colour, the surface on which it is resting being red and the two transverse 
sides dark, you will see the natural colour of this object take on the hues 
of those colours which are over against it. The strongest will be that 
proceeding from the light, the second that from the illuminated wall, 
the third that of the shadow. There yet remains however a portion 
which will take its hue from the colour of the edges. 

The supreme misfortune is when theory outstrips performance. 

In the choice of figures aim at softness and delicacy rather than that 
they should be stiff and wooden. 


That body will present the strongest contrast between its lights and 
shadows which is seen by the strongest light, such as the light of the sun 
or at night by the light of a fire; but this should rarely be employed in 
painting, because the work will remain hard and devoid of grace. 

A body which is in a moderate light will have but little difference 
between its lights and shadows; and this comes to pass at the fall of the 
evening, or when there are clouds: works painted then are soft in 
feeling and every kind of face acquires a charm. 

Thus in every way extremes are injurious. Excess of light makes 
things seem hard;^ and too much darkness does not admit of our seeing 
them. The mean is excellent. 

^ MS. has tl tropo lume fa crudo. So also Dr. Richter. The text of M. Ravaisson- 
Mollien has facendo in place of fa crudo, 



British Museum 

Royal Ldbrary, Windsor 



The lights cast from small windows also present a strong contrast 
of light and shadow, more especially if the chamber lit by them is large; 

and this is not good to use in painting. „ 

■ ^ o MS. 2038 Bib. Nat. 33 V. s 

The painter who draws by practice and judgment of the eye without 
the use of reason, is like the mirror that reproduces within itself all 
the objects which are set opposite to it without knowledge of the same. 

C.A. 76 r. a :i 

That countenance which in a picture is looking full in the face of 
the master who makes it will always be looking at all the spectators. 

And the figure painted when seen below from above will always appear 
as though seen below from above, although the eye of the beholder may 
be lower than the picture itself. 

^ C.A. 1 1 1 V. b i: 


If nature had only one fixed standard for the proportions of the | 

various parts, then the faces of all men would resemble each other to | 

such a degree that it would be impossible to distinguish one from 
another; but she has varied the five parts of the face in such a way that 
although she has made an almost universal standard as to their size, she 
has not observed it in the various conditions to such a degree as to 
prevent one from being clearly distinguished from another. 

C.A. 1 19 V. a 

As the body with great slowness produced by the length of its j 

contrary movement turns in greater space and thereby gives a stouter I 

blow, whereas movements which are continuous and short have little f 

strength — so study upon the same subject made at long intervals of J 

time causes the judgment to become more perfect and the better to 
recognise its own mistakes. And the same is true of the eye of the 
painter as it draws farther awav from his picture. 1 

A picture or any representation of figures ought to be done in such 
a way that those who see them may be able with ease to recognise from 
their attitudes what is passing through their minds. So if you have to 
represent a man of good repute in the act of speaking, make his gestures 
accord with the probity of his speech; and similarly if you have to 
represent a brutal man, make him with fierce movements flinging out 


his arms towards his hearer, and the head and chest protruding forward 
beyond the feet should seem to accompany the hands of the speaker. 

Just so a deaf mute who sees two people talking, although being 
himself deprived of the power of hearing, is none the less able to divine 
from the movements and gestures of the speakers the subject of their 

I once saw in Florence a man who had become deaf, who could not 
understand you if you spoke to him loudly, while if you spoke softly 
without letting the voice utter any sound, he understood you merely 
from the movement of the lips. Perhaps, however, you will say to me: 
‘But does not a man who speaks loudly move his lips like one who speaks 
softly.? And since the one moves his lips like the other, will not the one 
be understood like the other?’ As to this I leave the decision to the test 
of experience. Set someone to speak softly and then [louder], and watch 


How from age to age the art of painting continually declines and 
deteriorates when painters have no other standard than work already 

The painter will produce pictures of little merit if he takes the works 
of others as his standard; but if he will apply himself to learn from the 
objects of nature he will produce good results. This we see was the 
case with the painters who came after the time of the Romans, for they 
continually imitated each other, and from age to age their art steadily 

After these came Giotto the Florentine, and he — reared in mountain 
solitudes, inhabited only by goats and such like beasts — turning straight 
from nature to his art, began to draw on the rocks the movements of the 
goats which he was tending, and so began to draw the figures of all the 
animals which were to be found in the country, in such a way that after 
much study he not only surpassed the masters of his own time but all 
those of many preceding centuries. After him art again declined, because 
all were imitating paintings already done; and so for centuries it con- 
tinued to decline until such time as Tommaso the Florentine, nick- 
named Masaccio, showed by the perfection of his work how those who 
took as their standard anything other than nature, the supreme guide of 
all the masters, were wearying themselves in vain. Similarly I would say 
about these mathematical subjects, that those who study only the 

. 276 . 


authorities and not the works of nature are in art the grandsons and not 
the sons of nature, which is the supreme guide of the good authorities, 
Mark the supreme folly of those who censure such as learn from 
nature, leaving uncensured the authorities who were themselves the 
disciples of this same nature! 

^ C.A. IJ.I T. b 


Of not regarding the limbs of the figures in historical subjects, as 
many do who in making whole figures spoil their arrangement. For 
when you make figures one behind another, see that you draw them in 
their entirety, so that the limbs which are seen appearing beyond the 
surface of the first figure may retain their natural length and position. 

When a man running wishes to use up the impetus which is carrying 
him on, he prepares a contrary impetus which is brought into operation 
by his leaning backwards; this is capable of proof, for if the impetus 
carries the moving body forward with a momentum represented by 
four, and the impulse of the moving body to turn and fall back has a 
momentum of four the one momentum will neutralise the other which is 
contrary to it, and so the impetus is used up. 


The surface of each body takes part of the colour of whatever is set 
against it. The colours of the objects in light are reproduced on each 
other’s surface at different spots according to the varieties in the positions 
of these objects. [Diagram] Let o be a blue object in light, which alone 
by itself faces the space b of the white sphere a b c d ef^ and tinges it 
blue; and let w be a yellow object which is reflected on the space a b’m 
company with the blue object and tinges it green, by the second of this 
which shows that blue and yellow together produce a most beautiful 
green, etc. — and the rest will be set forth in the Book on Painting. In 
that book it will be demonstrated, by transmitting the images of the 
bodies and colours of the things illuminated by the sun through a small 
round hole in a dark place on to a smooth surface which in itself is 
white. But everything will be upside down. ^ ^ 

c.A. i8i r. a 



The painter requires such knowledge of mathematics as belongs to 
painting, and severance from companions who are notin sympathy with 
his studies, and his brain should have the power of adapting itself to the 
tenor of the objects which present themselves before it, and he should be 
freed from all other cares. 

And if while considering and examining one subject a second should 
intervene, as happens when an object occupies the mind, he ought to 
decide which of these subjects presents greater difficulties in investiga- 
tion, and follow that until it becomes entirely clear, and afterwards 
pursue the investigation of the other. And above all he should keep his 
mind as clear as the surface of a mirror, which becomes changed to as 
many different colours as are those of the objects within it, and his com- 
panions should resemble him in a taste for these studies, and if he fail to 
find any such he should accustom himself to be alone in his investiga- 
tions, for in the end he will find no more profitable companionship. 

C A. 184 V. C 


I say that one ought first to learn about the limbs and how they are 
worked, and after having completed this knowledge one ought to study 
their actions in the different conditions in which men are placed, and 
thirdly to devise figure compositions, the studies for these being taken 
from natural actions made on occasion as opportunities offered ; and one 
should be on the watch in the streets and squares and fields, and there 
make sketches with rapid strokes to represent features, that is for a head 
one may make an 0, and for an arm a straight or curved line, and so in 
like manner for the legs and trunk, afterwards when back at home work- 
ing up these notes in a completed form. 

My opponent says that in order to gain experience and to learn how 
to work readily, it is better that the first period of study should be spent 
in copying various compositions made by different masters either on 
sheets of paper or on walls, since from these one acquires rapidity in 
execution and a good method. But to this it may be replied that the 
ensuing method would be good if it was founded upon works that were 
excellent in composition and by diligent masters; and since such masters 
are so rare that few are to be found, it is safer to go direct to the works of 
nature than to those which have been imitated from her originals with 

27.8 . 



great deterioration and thereby to acquire a bad method, for he who has 
access to the fountain does not go to the water-pot. 

° ^ C.A. 199 V. a 

These rules are to be used solely in testing figures; for every man in 
his first compositions makes certain mistakes, and if he does not become 
conscious of them he does not correct them; therefore in order to dis- 
cover mistakes you should test your work and where you find there mis- 
takes correct them, and remember never to fall into them again. But if 
you were to attempt to apply all these rules in composition you would 
never make a beginning and would cause confusion in your work. 

These rules are intended to help you to a free and good judgment; 
for good judgment proceeds from good understanding, and good under- 
standing comes from reason trained by good rules, and good rules are 
the children of sound experience, which is the common mother of all 
the sciences, and arts. If therefore you bear well in mind the precepts 
of my rules you will be able merely by the accuracy of your judgment 
to criticize and discern every error in proportion in any work, whether 
it is in the perspective or in the figures or other things. 221 v d 

All the limbs of every kind of animal should correspond with its age, 
that is, the young should not show their veins or nerves as most [painters] 
do in order to show their dexterity in art, spoiling the whole by mistakes 
in the limbs. 

All the parts of an animal should correspond with the whole, that is, 
when a man is short and thickset you must see that each of his limbs is 
short and thickset. 

Let the movements of men be such as are in keeping with their 
dignity or meanness. c.A. 345 v.b 

Make your work to be in keeping with your purpose and design; 
that is, when you make your figure you should consider carefully who it 
is and what you wish it to be doing. 

In order to produce an effect of similar action in a picture of 
an old man and a young, you must make the action of the young 
man appear more vigorous in proportion as he is more powerful than 
the old man, and you will make the same difference between a young 
man and an infant. 


If you have to represent a man either as moving or lifting or pulling, 
or carrying a weight equal to his own weight, how ought you to fit the 
legs under his body? c.A.349 r.b 

Painters oftentimes deceive themselves by representing water in 
which they render visible what is seen by man; whereas the water sees the 
object from one side and the man sees it from the other; and it frequently 
happens that the painter will see a thing from above and the water sees it 
from beneath, and so the same body is seen in front and behind, and 
above and below, for the water reflects the image of the object in one way 
and the eye sees it in another. , 

J C.A. 354 r. d 

We consider as a monstrosity one who has a very large head and short 
legs, and as a monstrosity also one who is in great poverty and has rich 
garments; we should therefore deem him well proportioned in whom the 
parts are in harmony with the whole. 

A J C.A. r. c 

A S T O T H E L I M B S 

The painter who has clumsy hands will reproduce the same in his 
works, and the same thing will happen with every limb unless long study 
prevents it. Do you then, O painter, take careful note of that part in 
yourself which is most mis-shapen, and apply yourself by study to 
remedy this entirely. For if you are brutal, your figures will be the same 
and devoid of grace, and in like manner every quality that there is 
within you of good or of evil will be in part revealed in your figures. 

A 23 r. 

When you draw nudes be careful always to draw the whole figure, 
and then finish the limb which seems the best and at the same time study 
its relation to the other limbs, as otherwise you may form the habit of 
never properly joining the limbs together. 

Take care never to make the head turn the same way as the chest 
nor the arm move with the leg; and if the head is turned towards the 
right shoulder make all the parts lower on the left side than on the right, 
but if you make the chest prominent and the head turning on the left 
side, then make the parts on the right side higher than those on the left. 

A 28 V. 


Note in the movements and attitudes of the figures how the limbs 
and their expressions vary, because the shoulder blades in the movements 
of the arms and shoulders alter considerably the position of the back- 
bone; and you will find all the causes of this in my book of Anatomy. 

O F S H A D O W S A N D L I G H T s 

You, who reproduce the works of nature, behold the dimensions, the 
degrees of intensity, and the forms of the lights and shadows of each 
muscle, and observe in the lengths of their figures towards which muscle 
they are directed by the axis of their central lines. 

: A ■ , B 3 r. 

I N P A I N T I N G 

The background that surrounds the figures in any subject composi- 
tion ought to be darker than the illuminated part of these figures, and 
lighter than their part in shadow. E4r ^ 

That every part of a whole should be in proportion to its whole: 
thus if a man has a thick short figure that he should be the same in 
every one of his limbs, that is, with short thick arms, big hands, fingers 
thick and short, with joints of the same character and so with the rest. 

, And I would have the same understood to apply to all kinds of animals 

and plants; thus, in diminishing the parts, do so in proportion to their 
size, as also in enlarging. j 

si'".. . . . " ■ ■ ■ ■ ■ ■" ■ ' ' ■ I 


In representing wind, in addition to showing the bending of the 
boughs and the inverting of their leaves at the approach of the wind, 

^ you should represent the clouds of fine dust mingled with the troubled j 


I The first requisite of painting is that the bodies which it represents 

should appear in relief, and that the scenes which surround them with 
effects of distance should seem to enter into the plane in which the pic- 
ture is produced by means of the three parts of perspective, namely the 
diminution in the distinctness of the form of bodies, the diminution in 
their size, and the diminution in their colour. Of these three divisions of 

28 t 


perspective, the first has its origin in the eye, the two others are derived 
from the atmosphere that is interposed between the eye and the objects 
which the eye beholds. 

The second requisite of painting is that the actions should be appro- 
priate and have a variety in the figures, so that the men may not all look 
as though they were brothers. ^ 


The painter ought to strive at being universal, for there is a great 
lack of dignity in doing one thing well and another badly, like many 
who study only the measurements and proportions of the nude figure 
and do not seek after its variety; for a man may be properly propor- 
tioned and yet be fat and short or long and thin, or medium. And who- 
ever does not take count of these varieties will always make his figures 
in one mould, so that they will all appear sisters, and this practice deserves 
severe censure. 


It is an easy matter for whoever knows how to represent man to 
afterwards acquire this universality, for all the animals which live upon 
the earth resemble each other in their limbs, that is in muscles, sinews 
and bones, and they do not vary at all, except in length or thickness as 
will be shown in the Anatomy. There are also the aquatic animals, of 
which there are many different kinds; but with regard to these I do not 
advise the painter to make a fixed standard, for they are of almost infinite 
variety; and the same is also true of the insect world. 

The air was dark from the heavy rain which was falling slantwise, 
bent by the cross-current of the winds, and formed itself in waves in the 
air, like those one sees formed by the dust, the only difference being that 
these drifts were furrowed by the lines made by the drops of the falling 
water. It was tinged by the colour of the fire produced by the thunder- 
bolts wherewith the clouds were rent and torn asunder, the flashes from 
which smote and tore open the vast waters of the flooded valleys, and as 


these lay open there were revealed their depths^ the bowed tops of 
the trees. 

Neptune might be seen with his trident in the midst of the waters, 
and iEolus with his winds should be shown entangling the floating trees 
which had been uprooted and were mingled with the mighty waves. 

The horizon and the whole firmament was overcast and lurid with 
the flashings of the incessant lightning. 

Men and birds might be seen crowded together upon the tall trees 
which over-topped the swollen waters, forming hills which surround the 
great abysses. g 6v 


Those who are enamoured of practice without science are like a 
pilot who goes into a ship without rudder or compass and never has any 
certainty where he is going. 

Practice should always be based upon a sound knowledge of theory, 
of which perspective is the guide and gateway, and without it nothing 
can be done well in any kind of painting. ^ g 

Of the lights on the lower extremities of bodies packed tightly 
together, such as men in battle: 

Of men and horses labouring in battle, the different parts should be 
darker in proportion as they are closer to the ground on which they are 
supported; and this is proved from the sides of wells, which become 
darker in proportion to their depth, this being due to the fact that the 
lowest part of the well sees and is seen by a lesser amount of the luminous 
atmosphere than any other part of it. And the pavements when they 
are the same colour as the legs of the men and horses will always seem in 
higher light within equal angles than will these same legs. g 15 r 


First you should consider the figures whether they have the relief 
which their position requires, and the light that illuminates them, so that 
the shadows may not be the same at the extremities of the composition 

^ Dr, Richter reads vertici. I have followed M. Ravaisson-Moilien in reading 
ventri, MS. has vertri. 

® At margin of MS., ‘See first the [Ars] Poetica of Horace*. 



as in the centre, because it is one thing for a figure to be surrounded by 
shadows, and another for it to have the shadows only on one side. 
Those figures are surrounded by shadows which are towards the 
centre of the composition, because they are shaded by the dark figures 
interposed between them and the light; and those are shaded on one side 
only which are interposed between the light and the main group, for 
where they do not face the light they face the group, and there they 
reproduce the darkness cast by this group, and where they do not face 
the group they face the brightness of the light, and there they reproduce 
its radiance. 

Secondly, you should consider whether the distribution or arrange- 
ment of the figures is devised in agreement with the conditions you 
desire the action to represent. 

Thirdly, whether the figures are actively engaged on their purpose. 

G 19 r. 

O F P A I N T I N G 

A very important part of painting consists in the backgrounds of the 
things painted. Against these backgrounds the contour lines of such 
natural bodies as possess convex curves will always reveal the shapes of 
these bodies, even though the colours of the bodies are of the same hue 
as the background. 

This arises from the fact of the convex boundaries of the objects not 
being illuminated in the same manner as the background is by the same 
light, because frequently the contours are clearer or darker than the 

Should however these contours be of the same colour as the back- 
ground, then undoubtedly this part of the picture will interfere with the 
perception of the figure formed by these contour lines. Such a predica- 
ment in painting ought to be avoided by the judgment of good painters, 
since the painter’s intention is to make his bodies appear detached from 
the background; and in the above-mentioned instance the contrary 
occurs, not only in the painting but in the objects in relief. g 23 v 


There are many men who have a desire and love for drawing but 
no aptitude for it, and this can be discerned in children if they are not 
diligent and never finish their copies with shading. 

Extyal Library^ Windsor 


The painter is not worthy of praise who does only one thing well, as 
the nude, or a head, or draperies, or animal life, or landscapes, or such 
other special subject; for there is no one so dull of understanding that 
after devoting himself to one subject only and continually practising 
at this, he will fail to do it well. 

G 25 r. 

\The representation of things in movement^ 

Of the imitation of things which though they have movement in their 
own place, do not in this movement reveal themselves as they are in 

Drops of water when it rains, a winder, the turning-wheel, stones 
under the action of water, firebrands whirled round in a circle, proceed 
continuously, among things which are not in continuous movement. 

O F A L L T H I N G S 

The truth of this proposition is proved by the fact that the boundary 
of the substance is a surface, which is neither a part of the body enclosed 
by this surface nor a part of the atmosphere which surrounds this body, 
but is the medium interposed between the atmosphere and the body, as is 
proved in its place. 

But the lateral boundaries of these bodies are the boundary line of 
the surface, which line is of invisible thickness. Therefore, O painter, 
do not surround your bodies with lines, and especially when making 
objects less than their natural size, for these not only cannot show their 
lateral boundaries, but their parts will be invisible, from distance. 


The high lights or the lustre of any particular object will not be 
situated in the centre of the illuminated part, but will make as many 
changes of position as the eye that beholds it. ^ ^ 

Painters have a good opportunity of observing actions in players, 
especially at ball or tennis or with the mallet when they are contending 
together, better indeed than in any other place or exercise. ^ ^ 


It is the extremities of all things which impart to them grace or lack 

of grace. ^ 9 ^ [ 44 ] v. 

Men and words are actual, and you, painter, if you do not know how 
to execute your figures, will be like an orator who does not know 
how to use his words. kiio [3o]v. 

It is a necessary thing for the painter, in order to be able to fashion 
the limbs correctly in the positions and actions which they can represent 
in the nude, to know the anatomy of the sinews, bones, muscles and 
tendons in order to know, in the various different movements and im- 
pulses, which sinew or muscle is the cause of each movement, and to make 
Lly these prominent and thickened, and not the others all over the 
limb, as do many who in order to appear great draughtsmen make their 
nudes wooden and without grace, so that it seems rather as if you were 
looking at a sack of nuts than a human form or at a bundle of radishes 
rather than the muscles of nudes. 1791. 

In all things seen one has to consider three things, namely the position 
of the eye that sees, the position of the object seen and the position of the 
light that illumines this body. mSot, 

In thefalt folds of the joints of any limb everything whiA was in 
relief becomes a hollow, and similarly every hollow in the last of the sai 
folds is changed into a protuberance when the end of the limb is 

has not knowledge of this, often makes very great mistakes 
through relying too much upon his own skill, and not having recourse 
to the imitation of nature. And such variation is found more in the 
middle of the sides than in front and more behind than at the sides. 

B.M. 44 r. 

The painter contends with and rivals nature. Forster in 44 v, 

\On draperies\ . . , u -i-u 

Variety in the subjects. The draperies thin, thick, new, old, with 
folds broken and pleated, cride dolci [.^soft lights], shadows obscme and 
less obscure, either with or without reflections, definite or indistinct 

286 ■ ■ 


according to the distances and the various colours; and garments accord- 
ing to the rank of those who are wearing them, long and short, fluttering 
or stiff in conformity with the movements; so encircling the figures as 
to bend or flutter with ends streaming upwards or downwards according 
to the folds, clinging close about the feet or separated from them, 
according as the legs are shown at rest or bending or twisting or strik- 
ing together within; either fitting closely or separating from the joints, 
according to the step or movement or whether the wind is represented. 
And the folds should correspond to the quality of the draperies 
whether transparent or opaque. 

[Repetition — the greatest defect in a painter^ 

The greatest defect in a painter is to repeat the same attitudes and 
the same expressions ... in one ... 

[On draperiesi 

On the thin clothes of the women in walking, running and jumping, 

and their variety. 

[Notes on paintingl 

And in painting make a discourse on the clothes and other raiments. 

And you, O painter, who desire to perform great things, know that 
unless you first learn to do them well and with good foundations, the work 
that you do will bring you very little honour and less gain, but if you 
do it well it will produce you plenty of honour and be of great utility. 

Quaderni iv 15 r. 

When the subject of your picture is a history make two points, one 
of the eye and the other of the light, and make the latter as far distant as 
possible. Windsor: Drawings 12604 r. 

Nature of movements in man. Do not repeat the same actions in the 
limbs of men unless the necessity of their action constrains you. 

Windsor: Drawings 191 49 V. 

I N P A I N T I N G 

Let the dark, gloomy air be seen beaten by the rush of opposing 
winds wreathed in perpetual rain mingled with hail,^ and beariim hither 
and thither a vast network of the torn branches of trees mixed ^ether 
^ MS. gravza. I have followed Dr. Richter’s suggestion gragmok, M 


with an infinite number of leaves. All around let there be seen ancient 
trees uprooted and torn in pieces by the fury of the winds. You should 
show how fragments of mountains, which have been already stripped 
bare by the rushing torrents, fall headlong into these very torrents and 
choke up the valleys, until the pent-up rivers rise in flood and cover the 
wide plains and their inhabitants. Again there might be seen huddled 
together on the tops of many of the mountains many different sorts of 
animals, terrified and subdued at last to a state of tameness, in company 
with men and women who had fled there with their children. And the 
fields which were covered with water had their waves covered over in 
great part with tables, bedsteads, boats and various other kinds of rafts, 
improvised through necessity and fear of death, upon which were men 
and women with their children, massed together and uttering various 
cries and lamentations, dismayed by the fury of the winds which were 
causing the waters to roll over and over in mighty hurricane, bearing 
with them the bodies of the drowned; and there was no object that floated 
on the water but was covered with various different animals who had 
made truce and stood huddled together in terror, among them being 
wolves, foxes, snakes and creatures of every kind, fugitives from death. 
And all the waves that beat against their sides were striking them with 
repeated blows from the various bodies of the drowned, and the blows 
were killing those in whom life remained. 

Some groups of men you might have seen with weapons in their hands 
defending the tiny footholds that remained to them from the Hons and 
wolves and beasts of prey which sought safety there. Ah, what dreadful 
tumults one heard resounding through the gloomy air, smitten by the 
fury of the thunder and the lightning it flashed forth, which sped 
through it, bearing ruin, striking down whatever withstood its course! 
Ah, how many might you have seen stopping their ears with their hands 
in order to shut out the loud uproar caused through the darkened air 
by the fury of the winds mingled together with the rain, the thunder of 
the heavens and the raging of the thunderbolts! Others were not content 
to shut their eyes, but placing their hands over them, one above the 
other, would cover them more tightly in order not to see the pitiless 
slaughter made of the human race by the wrath of God. 

Ah me, how many lamentations! How many in their terror flung 
themselves down from the rocks! You might have seen huge branches of 
the giant oaks laden with men borne along through the air by the fury 


Royal Library, Windsor 


of the impetuous winds. How many boats were capsized and lying, some 
whole, others broken in pieces, on the top of men struggling to escape 
with acts and gestures of despair which foretold an awful death. Others 
with frenzied acts were taking their own lives, in despair of ever being 
able to endure such anguish; some of these were flinging themselves 
down from the lofty rocks, others strangled themselves with their own 
hands; some seized hold of their own children, and with mighty violence 
slew them at one blow; some turned their arms against themselves to 
wound and slay; others falling upon their knees were commending 
themselves to God. 

Alas! how many mothers were bewailing their drowned sons, holding 
them upon their knees, lifting up open arms to heaven, and with divers 
cries and shrieks declaiming against the anger of the gods! Others with 
hands clenched and fingers locked together gnawed and devoured them 
with bites that ran blood, crouching down so that their breasts touched 
their knees in their intense and intolerable agony. 

Herds of animals, such as horses, oxen, goats, sheep, were to be seen 
already hemmed in by the waters and left isolated upon the high peaks 
of the mountains, all huddling together, and those in the middle climb- 
ing to the top and treading on the others, and waging fierce battles with 
each other, and many of them dying from want of food. 

And the birds had already begun to settle upon men and other 
animals, no longer finding any land left unsubmerged which was not 
covered with living creatures. Already had hunger, the minister of death, 
taken away their life from the greater number of the animals, when the 
dead bodies already becoming lighter began to rise from out the bottom 
of the deep waters, and emerged to the surface among the contending 
waves; and there lay beating one against another, and as balls puffed up 
with wind rebound back from the spot where they strike, these fell back 
and lay upon the other dead bodies. 

And above these horrors the atmosphere was seen covered with 
murky clouds that were rent by the jagged course of the raging thunder- 
bolts of heaven, which flashed light hither and thither amid the obscurity 
of the darkness. 

The velocity of the air is seen by the movement of the dust stirred 
by the running of a horse; and it moves as swiftly to fill up the void left 
in the air which had enclosed the horse as is the speed of the horse in 
passing away from the aforesaid space of air. 


But it will perhaps seem to you that you have cause to censure me 
for having represented the different courses taken in the air by the move- 
ment of the wind, whereas the wind is not of itself visible in the air; to 
this I reply that it is not the movement of the wind itself but the move- 
ment of the things carried by it which alone is visible in the air. 

The divisions 

Darkness, wind, tempest at sea, deluge of water, woods on fire, rain, 
thunderbolts from the sky, earthquakes and destruction of mountains, 
levelling of cities. 

Whirlwinds which carry water and branches of trees and men 
through the air. 

Branches torn away by the winds crashing together at the meeting 
of the winds, with people on the top of them. 

Trees broken off laden with people. 

Ships broken in pieces dashed upon the rocks. 

Hail, thunderbolts, whirlwinds. 

Herds of cattle. 

People on trees which cannot bear them: trees and rocks, towers, 
hills crowded with people, boats, tables, troughs and other contrivances 
for floating, — hills covered with men and women and animals, with 
lightnings from the clouds which illumine the whole scene. 

Windsor: Drawings 12665 v. 


First of all let there be represented the summit of a rugged mountain 
with certain of the valleys that surround its base, and on its sides let the 
surface of the soil be seen slipping down together with the tiny roots of 
the small shrubs, and leaving bare a great part of the surrounding rocks. 
Sweeping down in devastation from these precipices, let it pursue its 
headlong course, striking and laying bare the twisted and gnarled roots 
of the great trees and overturning them in ruin. And the mountains 
becoming bare should reveal the deep fissures made in them by the 
ancient earthquakes; and let the bases of the mountains be in great part 
covered over and clad with the debris of the shrubs which have fallen 
headlong from the sides of the lofty peaks of the said mountains, and let 
these be mingled together with mud, roots, branches of trees, with 
various kinds of leaves thrust in among the mud and earth and stones. 
And let the fragments of some of the mountains have fallen down intg 


■ ' ' . : 1 , . 

Royal JUbraryt Windsor 


the depth of one of the valleys, and there form a barrier to the swollen 
waters of its river, which having already burst the barrier rushes on with 
immense waves, the greatest of which are striking and laying in ruin the 
walls of the cities and farms of the valley. And from the ruins of the lofty 
buildings of the aforesaid cities let there rise a great quantity of dust, 
mounting up in the air with the appearance of smoke or of wreathed 
clouds that battle against the descending rain. 

But the swollen waters should be coursing round the pool which con- 
fines them, and striking against various obstacles with whirling eddies, 
leaping up into the air in turbid foam, and then falling back and causing 
the water where they strike to be dashed up into the air; and the circling 
waves which recede from the point of contact are impelled by their 
impetus right across the course of the other circling waves which move 
in an opposite direction to them, and after striking against these they 
leap up into the air without becoming detached from their base. 

And where the water issues forth from the said pool, the spent waves 
are seen spreading out towards the outlet; after which, falling or descend- 
ing through the air, this water acquires weight and impetus; and then 
piercing the water where it strikes, it tears it apart and dives down in 
fury to reach its depth, and then recoiling, it springs back again towards 
the surface of the lake accompanied by the air which has been submerged 
with it, and this remains in the slimy foam^ mingled with the driftwood 
and other things lighter than the water, and around these again are 
formed the beginnings of the waves, which increase the more in circum- 
ference as they acquire more movement; and this movement makes them 
lower in proportion as they acquire a wider base, and therefore they 
become almost imperceptible as they die away. But if the waves rebound 
against various obstacles then they leap back and oppose the approach 
of the other waves, following the same law of development in their 
curve as they have already shown in their original movement. The rain 
as it falls from the clouds is of the same colour as these clouds, that is on 
its shaded side, unless, however, the rays of the sun should penetrate 
there, for if this were so the rain would appear less dark than the cloud. 
And if the great masses of the debris of huge mountains or of large 
buildings strike in their fall the mighty lakes of the waters, then a vast 
quantity of water will rebound in the air, and its course will be in an 

^ Richter’s transcript (§ 609) is ‘vissci cholla’, and he reads ‘nella umta colla sciuma’. 
The MS. haSy I think, Visscichosa’, which I have taken as a variant of ‘vischiosa’, 

■ 291 ■ ■■■ 


opposite direction to that of the substance which struck the water, that 
is to say the angle of reflection will be equal to the angle of incidence. 

Of the objects borne along by the current of the waters, that will be 
at a greater distance from the two opposite banks which is heavier or of 
larger bulk. The eddies of the waters revolve most swiftly in those parts 
which are nearest to their centre. The crests of the waves of the sea fall 
forward to their base, beating and rubbing themselves against the smooth 
particles which form their face; and by this friction the water as it falls 
is ground up in tiny particles,^ and becomes changed to thick mist, and 
is mingled in the currents of the winds in the manner of wreathing smoke 
or winding clouds, and at last rises up in the air and becomes changed 
into clouds. But the rain which falls through the air, being beaten upon 
and driven by the current of the winds, becomes rare or dense according 
to the rarity or density of these winds, and by this means there is pro- 
duced throughout the air a flood of transparent clouds which is formed 
by the aforesaid rain, and becomes visible in it by means of the lines made 
by the fall of the rain which is near to the eye of the spectator. * The 
waves of the sea that beats against the shelving base of the mountains 
which confine it, rush® foaming in speed up to the ridge of these same 
hills, and in turning back meet the onset of the succeeding wave, and 
after loud roaring return in a mighty flood to the sea from whence they 
came. A great number of the inhabitants, men and different animals, 
may be seen driven by the rising of the deluge up towards the summits of 
the hills which border on the said waters. 

Waves of the sea at Piombino all of foaming water. 

Of the water that leaps up — [of the place where the great masses fall 
and strike the waters] * — of the winds of Piombino. 

Eddies of winds and of rain with branches and trees mingled with 
the air. 

The emptying the boats of the rain water. 

Windsor: Drawings 12665 r. 

^ MS., e ttal confreghafione trita in minute partichule la disscienfe acqua. 

® MS., ‘ce p(er) quessto si gienera infrallaria vna innondatione di trasspareti nuvoli la 
quale effacta dalla p{r)edetta pioggia e inquassta si fa manifessta mediante i liniameti fatti 
dal dissdeso della pioggia che e vidna all ochio che la vede’. The words printed in italics 
are wanting in the text as given by Dr. Richter (§ 609). 

® Dr. Richter reads saranno (for MS. sarrano)^ but the text is, I think, scorrano^ 
presumably for 

* The sentence within brackets is crossed through in the MS, 

292 ■ 


‘Make the perspective of the colours so that it 
is not at variance with the size of any object, 
that is, that the colours lose part of their nature 
in proportion as the bodies at different distances 
suffer loss of their natural quantity,’ 


Of colours of equal whiteness that will seem most dazzling which is 
on the darkest background, and black will seem most intense when it is 
against a background of greater whiteness. 

Red also will seem most vivid when against a yellow background, 
and so in like manner with all the colours when set against those which 
present the sharpest contrasts. „ 

G.A. 184 V. C 

The more white a thing is the more it will be tinged with the colour 
of the illuminated or luminous object. , 

C.A. 262 r. c 

But in the far distance that object will show itself most blue which is 
darkest in colour. 

C.A. 305 r. a 

Every object that has no colour in itself is tinged either entirely or in 
part by the colour [of the object] set opposite to it. This may be seen 
by experience, for every object which serves as a mirror is tinged with 
the colour of the thing that is reflected in it. And if the object which is 
in part tinged is white, the portion of it that is illumined by red will 
appear red, and so with every other colour whether it be light or dark. 

Every opaque object that is devoid of colour partakes of the colour of 
that which is opposite to it: as happens with a white wall. ^ j 


Note how spirit (acqua vite) collects in itself all the colours and 
scents of the flowers; and if you wish to make azure, put cornflowers 
and then wild poppies. 

[Of distant colour] 

The variation in the colours of objects at a great distance can only 
be discerned in those portions which are smitten by the solar rays. 

C 12 V. 

As regards the colours of bodies there is no difference at a great 
distance in the parts which are in shadow. 

A ' . ' . C T. " 



A dark object will appear more blue when it has a larger amount of 
luminous atmosphere interposed between it and the eye, as may be seen 
in the colour of the sky. c i8 r 

[A discussion on the colours of shadows\ 


Colours seen in shadow will reveal more or less of their natural 
beauty in proportion as they are in fainter or deeper shadow. 

But if the colours happen to be in a luminous space they will show 
themselves of greater beauty in proportion as the luminosity is more 


The varieties in the colours of shadows are as numerous as the 
varieties in colour of the objects which are in the shadows. 


Colours seen in shadow will reveal less variety one with another 
according as the shadows wherein they lie are deeper. There is evidence 
of this from those who from a space without peer within the doorways of 
shadowy temples, for there the pictures clad as they are in divers colours 
all seem robed in darkness. 

So therefore at a long distance all the shadows of different colours 
appear of the same darkness. 

Of bodies clad in light and shade it is the illuminated part which 
reveals the true colour. 

E i8 r. 

No white or black is transparent. 

^ F 23 r. 


Since white is not a colour but is capable of becoming the recipient 
of every colour, when a white object is seen in the open air all its shadows 
are blue; and this comes about in accordance with the fourth proposition, 
which says that the surface of every opaque body partakes of the colour 
of surrounding objects. As therefore this white object is deprived of the 
light of the sun by the interposition of some object which comes between 
the sun and it, all that portion of it which is exposed to the sun and the 
atmosphere continues to partake of the colour of the sun and the atmo- 


I ' ' 


sphere, and that part which is not exposed to the sun remains in shadow, 
and partakes only of the colour of the atmosphere. 

And if this white object should neither reflect the green of the fields 
which stretch out to the horizon nor yet face the brightness of the horizon 
itself, it would undoubtedly appear of such simple colour as the atmo- 
sphere showed itself to be. 

F 75 r. 


The accidental colours of the leaves of trees are four, namely 
shadow, light, lustre and transparency. 


The accidental parts of the leaves of plants will at a great distance 
become a mixture, in which the accidental colour of the largest will pre- 

G 24 r. 

O F P A I N T I N G 

The colour of the object illuminated partakes of the colour of that 
which illuminates it. 

. ^ ^ 37 r- 

The surface of every body participates in the colour of the body that 
illuminates it: 

And in the colour of the air that is interposed between the eye and 
this body, that is to say in the colour of the transparent medium inter- 
posed between the object and the eye. 

Among colours of the same quality, the second will never be of the 
same colour as the first; and this proceeds from the multiplication of the 
colour of the medium interposed between the object and the eye. 

G 53 V. 

Of the various colours other than blue, that which at a great distance 
will resemble blue most closely will be that which is nearest to black, 
and so conversely the colour which least resembles black will be the one 
which at a great distance will most retain its natural colour. 

Accordingly, the green in landscapes will become more changed into 
blue than will the yellow or the white, and so conversely the yellow and 
the white will undergo less change than the green, and the red still less. 

L7S V. 



The shadow of flesh should be of burnt /^rr^ verde. 

92 r 

Quaderni iv 3 r. 

The image imprinted in a mirror partakes of the colour of the said 


The surface of every dark body will participate in the colour of the 
bodies placed against it. Forster m 74 v. 

The surface of every opaque body will be capable of participating 
and will be tinged with the colour of the bodies placed against it. 

Forster in 75 r. 


\The apparent colours of smoke on the horizon^ 

The density of smoke from the horizon downwards is white and from 
the horizon upwards it is dark; and, although this smoke is in itself of the 
same colour, this equality shows itself as different, on account of the 
difference of the space in which it is found. 

[Colour of flamel 

As flame extends it becomes yellow in its upper part, then saffron in 
colour, and this ends in smoke. ^ 


The surface of every opaque body participates in the colour of its 

The surface of the opaque body is the more completely steeped in 
the colour of its object, in proportion as the rays of the images of these 
objects strike the objects at more equal angles. 

And the surface of opaque bodies is more steeped in the colour of 
their object, in proportion as this surface is whiter, and the colour of the 
object more luminous or illuminated. j • 

Quaderm vi 22 r. 


The colours of the rainbow are not created by the sun, because in 
many ways these colours are produced without the sun, as happens when 
you hold up a glass of water close to the eye, for in the glass of it there 
are the tiny bubbles which are usually seen in glass that is imperfectly 
refined. And these bubbles although they are not in sunlight will pro- 

■ 298 


duce on one side all the colours of the rainbow; and this you will see if 
you place the glass between the atmosphere and your eye in such a way 
as to be in contact with the eye, the glass having one side exposed to the 
light of the atmosphere, and on the other the shadow' of the wall on the 
right or left side of the window, which side does not matter. So by turn- 
ing this glass round you will see the aforesaid colours round about these 
bubbles in the glass. And we will speak of other methods in their place. 


The eye in the experiment described above would seem to have 
some share in the creation of the colours of the rainbow, because the 
bubbles in the glass do not display these colours except through the 
medium of the eye. But if you place this glass full of water on the level 
of the window, so that the sun’s rays strike it on the opposite side, you 
will then see the aforesaid colours producing themselves, in the impression 
made by the solar rays which have penetrated through this glass of 
water, and terminated upon the floor in a dark place at the foot of the 
window; and since here the eye is not employed we clearly can say with 
certainty that these colours do not derive in any way from the eye. 


There are many birds in the various regions of the world in whose 
feathers most radiant colours are seen produced in their different move- 
ments, as is seen happen among us with the feathers of peacocks, or on 
the necks of ducks or pigeons. 

Moreover on the surface of ancient glass found buried, and in the 
roots of radishes which have been kept a long time at the bottom of 
wells or other stagnant water [we see] that each of these roots is sur- 
rounded by a sequence of colours like those of the rainbow. It is seen 
when some oily substance has spread on the top of water; as also in the 
solar rays reflected from the surface of a diamond or beryl. Also, in the 
facet of the beryl, every dark object which has as its background the 
atmosphere or other clear object is surrounded by this sequence of 
colours interposed between the atmosphere and the dark object; and so 
in many other ways which I leave because these suffice for this present 
theme. Windsor: Drawings 19150 r, 




‘Describe landscapes with wind and water and 
at the setting and rising of the sun/ 

Within the spaces between the rain one sees the redness of the sun, 
that is of the clouds interposed between the sun and the rain. 

The waves interposed between the rain and the eye never reveal to 
the eye the image of the darkness of this rain, and this is due to the fact 
that the side of the wave is not seen nor does it see the rain. 

And the clouds are of dark purple. o , 

C.A. 38 r. b 

Of things seen through the mist the part which is nearest to the 

extremities will be less visible, and so much less when they are more 

remote. u 

c.A. 76 r. b 

A mountain that stretches above a city which raises dust in the form 
of clouds, but the colour of this dust is varied by the colour of these 
clouds; and, where the rain is thickest, the colour of the dust is least visible; 
and, where the dust is thickest, the rain is least visible; and, where the rain 
is mingled with the wind and the dust, the clouds created by the rain are 
more transparent than those of the dust. 

And when the flames of the fire are mingled with clouds of smoke 
and steam this creates dark and very thick clouds. 

The rest of this discourse will be treated of clearly in the book of 

\With drawing 

The trees, smitten by the course of the winds, bend towards the 
place where the wind is moving, and after the wind has passed they bend 
in the opposite movement, that is in the reflex movement. 

The mighty fury of the wind, driven by the avalanches of the 
mountains above the yawning caverns, by means of the avalanches of 
the mountains which formed a covering to these caverns. c a 79 r c 

When rain is falling from broken clouds one sees the shadows of 
these clouds upon the earth interrupted by the part of the earth that 
is illuminated by the sun. 

O F T H E R A I N B o W 

When the sun is lower the arc has a larger circle, and when it k 
higher it will be the contrary. 


When the sun is in the west, hidden behind some small and thick 
cloud, then this cloud will be surrounded by a ruddy splendour. 

C.A. 97 V. a 

Why towers and campaniles at a great distance, although of uniform 
thickness, seem like inverted pyramids. 

This arises from the fact that the lower tracts of air being thick and 
misty veil them more completely, and the more an object is veiled the 
more the perception of its extremities is lost, and consequently the 
perception of the object tends to concentrate about its central line. 

C.A. 130 v. b 


In the houses of a city, where one observes that the divisions between 
them are clear when it is misty below, if the eye is above the level of 
the houses the lines of vision, as they descend in the space that is between 
house and house, plunge into mist which is more dense and therefore, 
being less transparent, seems whiter; and if one house is higher than 
another the reality is more to be discerned in the thinner air, and there- 
fore they seem more indistinct in proportion as they are less" elevated. 

C.A. 160 r. a 

This came about by reason of the clouds interposed between the 
earth and the sun, wherefore being in the west it grew red and with its 
ruddy glow lit as with a haze all the things visible to it, but so much more 
or less in proportion as these things were nearer or more remote. 

C,A. 165 V. b 

At the first hour of the day the atmosphere in the south near to the 
horizon has a dim haze of rose-flushed clouds; towards the west it grows 
darker, and towards the east the damp vapour of the horizon shows 
brighter than the actual horizon itself, and the white of the houses in the 
east is scarcely to be discerned, while in the south, the farther distant 
they are, the more they assume a dark rose-flushed hue, and even more 
so in the west; and with the shadows it is the contrary, for these disappear 
before the white. 

[....] in the east, and the tops of the trees are more visible than their 
bases, since the atmosphere is thicker lower down, and the structure 
becomes more indistinct at a height. 

And in the south, the trees may scarcely be distinguished by reason 
of the vapour which darkens in the west and grows clear in the east. 

C.A. i 76 r. b 



If between the eye and the horizon there intervenes the slope of a 
hill that drops towards the eye, and the eye finds itself at about the 
middle of the height of the slope then the hill will acquire darkness 
with every stage of its length. This is proved by the seventh of this 
which says; that plant will show itself darker which is seen more below; 
therefore the proposition is confirmed, because the hill shows from the 
centre downwards all its plants in the parts which are as much illumined 
by the brightness of the sky, as the part which is in shade is shaded by 
the darkness of the earth. For which reason it is necessary that these 
plants should be of moderate darkness, and from this point on towards 
the bases of the hills the plants are continually becoming brighter 
through the converse of the seventh proposition, for by this seventh 
proposition the nearer such plants are to the summit of the hill the more 
of necessity they become darker. And it follows that this darkness is not 
proportionate to the distance, from the eighth proposition which says: 
that thing will show itself darker which finds itself in finer air; and by 
the tenth: that will show itself darker which borders on the brighter 
background. ca.iS+v.c 

E V E N I N G O R M O R N I N G I N T H E M I S T 

Buildings seen at a great distance in the evening or morning through 
mist or heavy atmosphere, have only such portions in light as are 
illuminated by the sun which is then near the horizon, and the parts of 
those buildings which are not exposed to the sun remain almost the 
same dim neutral colour as the mist. 

Why the higher things situated at a distance are darker than the 
lower ones even though the mist is of uniform thickness: 

Of the things situated in mist or any other dense atmosphere, whether 
this arise from vapour or smoke or distance, that will be most visible which 
is the highest, and of things of equal height that will seem darkest which 
is against a background of the deepest mist. As happens with the eye /z, 
which beholding a b e, towers of equal height, sees c the summit of the 
first tower at r, situated below in the mist at two degrees of depth, and 
. ■■ 30s 


sees the summit of the centre tower b in only one degree of mist; there- 
fore the summit c will show itself darker than the summit of the tower b, 

E 3 V. 


The landscapes which occur in representations of winter should not 
show the mountains blue as one sees them in summer, and this is proved 
by the fourth part of this [chapter], where it is stated that of the moun- 
tains seen at a great distance that will seem a deeper blue in colour which 
is in itself darker; for when the trees are stripped of their leaves they 
look grey in colour, and when they are with their leaves they are green, 
and in proportion as the green is darker than the grey, the green will 
appear a more intense blue than the grey; and by the fifth part of this 
[chapter], the shadows of trees which are clad with leaves are as much 
darker than the shadows of those trees which are stripped of leaves as 
the trees clad with leaves are denser than those without leaves; and thus 
we have established our proposition. 

The definition of the blue colour of the atmosphere supplies the 
reason why landscapes are a deeper shade of blue in summer than in 

The shadows of trees set in landscapes do not seem to occupy the 
same positions in the trees on the left as in those on the right, and this 
especially when the sun is on the right or the left. This is proved by the 
fourth which states:— opaque bodies placed between the light and the 
eye will show themselves entirely in shadow; and by the fifth:— the eye 
that is interposed between the opaque body and the light sees the 
opaque body all illuminated; and by the sixth:— when the eye and 
the opaque body are interposed between the darkness and the light the 
body will be seen half in shadow and half in light. ^ ^ 

E Y E A N D T H E V I S I B L E 0 B J E C T 

The object will appear more or less distinct at the same distance, in 
proportion as the atmosphere interposed between the eye and this 
object is of greater or less clearness. 

Since therefore you are aware that the greater or less quantity of 
atmosphere interposed between the eye and the object causes the outlines 
of these objects to seem more or less blurred to the eye, you should 
represent the stages of loss of definition of these bodies in the same 



proportion to each other as that of their distances from the eye of the 

E 79 V. 

When the smoke from dry wood comes between the eye of the 
observer and some dark space it appears blue. 

So the atmosphere appears blue because of the darkness which is 
beyond it; and if you look towards the horizon of the sky you will see 
that the atmosphere is not blue, and this is due to its density; and so, at 
every stage as you raise your eye up from this horizon to the sky which 
is above you, you will find that the atmosphere will seem darker, and 
this is because a lesser quantity of air interposes between your eye and 
the darkness. 

And if you are on the top of a high mountain the atmosphere will 
seem darker above you, just in proportion as it becomes rarer between 
you and the said darkness; and this will be intensified at every successive 
stage of its height, so that at the last it will remain blue. 

That smoke will appear the bluest which proceeds from the driest 
wood, and is nearest to the place of its origin, and when it is seen against 
the darkest background with the light of the sun upon it. ^ jg r 

The smoke that penetrates through the air if it is thick, and rises out 
of great flame which is fed by damp wood, does not mingle with it but 
makes itself seem denser above than in the centre, and does this the more 
when the air is chilly; and the faint gleam that penetrates the air is always 
warm and always becoming fainter, and of the dust which passes through 
the air the finest rises the highest. 

Although leaves with a smooth surface are for the most part of the 
same colour on the right side as on the reverse, it so happens that the 
side exposed to the atmosphere partakes of the colour of the atmosphere, 
and seems to partake of its colour more closely in proportion as the eye 
is nearer to it and sees it more foreshortened. And the shadows will 
invariably appear darker on the right side than on the reverse, through 
the contrast caused by the high lights appearing against the shadow. 

The under side of the leaf, although its colour in itself may be 
the same as that of the right side, appears more beautiful; and this 
colour is a green verging upon yellow; and this occurs when the leaf is 
interposed between the eye and the light which illumines it from the 

: 307,. 




opposite side. Its shadows also are in the same positions as those on 
the opposite side. 

Therefore, O painter, when you make trees near at hand, remember 
that when your eye is somewhat below the level of the tree you will be 
able to see its leaves some on the right side and some on the reverse; 
and the right sides will be a deeper blue as they are seen more fore- 
shortened, and the same leaf will sometimes show part of the right side 
and part of the reverse, and consequently you must make it of two 
colours. j 

G 3 r. and 2 V. 

When there is one belt of green behind another, the high lights on 
the leaves and their transparent lights show more strongly than those 
which are against the brightness of the atmosphere. 

And if the sun illumines the leaves without these coming between 
it and the eye, and without the eye facing the sun, then the high lights 
and the transparent lights of the leaves are extremely powerful. 

It is very useful to make some of the lower branches, and these should 
be dark, and should serve as a background for the illuminated belts of 
green which are at some little distance from the first. 

Of the darker greens seen from below, that part is darkest which is 
nearest to the eye, that is to say which is farthest from the luminous 
atmosphere, ^ 

Never represent leaves as though transparent in the sun, because 
they are always indistinct; and this comes about because over the 
transparency of one leaf there will be imprinted the shadow of another 
leaf which is above it; and this shadow has definite outlines and a fixed 
density. .And sometimes it is the half or third part of the leaf which is 
in the shadow, and consequently the structure of such a leaf is indistinct, 
and the imitation of it is to be avoided. 

The upper branches of the spreading boughs of trees keep nearer to 
the parent bough than do those below. 

That leaf is less transparent which takes the light at a more acute 


Of the plants which take their shadows from the trees which grow 
among them, those which are in front of the shadow have their stalks 

308 ■ ■ . 


lighted up against a background of shadow, and the plants which are 
in shadow have their stalks dark against a light background, that is 
against a background which is beyond the shadow. 


Of the trees which are between the eye and the light, the part in 
front will be bright, and this brightness will be diversified by the 
ramification of the transparent leaves — as seen from the under side — 
with the shining leaves seen from the right side, and in the background, 
below and behind, the verdure will be dark, because it is cast in shadow 
by the front part of the said tree; and this occurs in trees which are 
higher than the eye. g 9 v 


When the leaves are interposed between the light and the eye, then 
that which is nearest to the eye will be the darkest,, and that farthest 
away will be the lightest, if they are not seen against the atmosphere; and 
this happens with leaves which are beyond the centre of the tree, that is 
in the direction of the light. 

O G 10 V. 

0 F T R E E S A N D T H E I R L I G H T i 

The true method of practice in representing country scenes, or I I 

should say landscapes with their trees, is to choose them when the sun ; 

in the sky is hidden, so that the fields receive a diffused light and not the ; 

direct light of the sun, for this makes the shadows sharply defined and ii 

very different from the lights. guv ^ 


The shadows of verdure always approximate to blue, and so it is 
with every shadow of every other thing, and they tend to this colour 
more entirely when they are farther distant from the eye, and less in 
proportion as they are nearer. 

The leaves which reflect the blue of the atmosphere always present 

themselves edgewise to the eye. 



The part illuminated will show more of its natural colour at a great 
distance when it is illuminated by the most powerful light. g i c r 


When the sun is in the east and the eye is looking down upon a city 
from above, the eye will see the southern part of the city with its roofs 
half in shadow and half in light, and so also with the northern part; 
but the eastern part will be all in shadow and the western part all in 


Landscapes ought to be represented so that the trees are half in 
light and half in shadow; but it is better to make them when the sun is 
covered by clouds, for then the trees are lighted up by the general light 
of the sky and the general shadow of the earth; and these are so much 
darker in their parts, in proportion as these parts are nearer to the middle 
of the tree and to the earth. 

G. 19 V. 

O F T R E E S T N T H E S o U T H 

When the sun is in the east, the trees in the south and north are 
almost as much in light as in shadow, but the total amount in light is 
greater in proportion as they are more to the west, and the total amount 
in shadow is greater in proportion as they are more to the east. 

O F M E A D O W S 

When the sun is in the east, the grasses in the meadows and the 
other small plants are of a most brilliant green, because they are trans- 
parent to the sun. This does not happen with the meadows in the west, 
and in those in the south and north the grasses are of a moderate 
brilliance in their green. 

° G 20 V. 


When the sun is in the east all the parts of trees which are illu- 
minated by it are of a most brilliant green; and this is due to the fact 
that the leaves illuminated by the sun within half our hemisphere. 


namely the eastern half, are transparent, while within the western 
semicircle the verdure has a sombre hue and the air is damp and heavy, 
of the colour of dark ashes, so that it is not transparent like that in the 
east, which is refulgent, and the more so as it is more full of moisture. 

The shadows of the trees in the east cover a large part of the tree, and 
they are darker in proportion as the trees are thicker with leaves. 

G 21 r. 


When the sun is in the east the trees seen towards the east will 
have the light surrounding them all around their shadows, except 
towards the earth, unless the tree has been pruned in the previous year; 
and the trees in the south and in the north will be half in shadow and 
half in light, and more or less in shadow or in light according as they are I 

more or less to the east or to the west. 

The fact of the eye being high or low causes a variation in the 
shadows and lights of trees, for when the eye is above, it sees the trees ( 

with very little shadow, and when below with a great deal of shadow. [ 

The different shades of green of plants are as varied as are their | 

■■ ■ , . ■ ';V , Gaiv.;" I 


When the sun is in the east the trees towards the west will appear to 
the eye with very little relief and of almost imperceptible grada- 
tion, on account of the atmosphere which lies very thick between - 

the eye and these trees, according to the seventh [part] of this [treatise]; 
and they are deprived of shadow, for although a shadow exists in each 
part of the ramification, it so happens that the images of shadow and t 

light which come to the eye are confused and blended together, and 
cannot be discerned through the smallness of their size. And the i 

highest lights are in the centre of the trees and the shadows are toward 
their extremities, and their separation is marked by the shadows in the 
spaces between these trees when the forests are dense with trees; and in 
i those which are more scattered the contours are but little seen. 

■ .G 22'r. ■.! 


When the sun is in the east the trees in that quarter are dark towards 
the centre, and their edges are in light. i 

• ' 311 i 



The smoke is seen better and more distinctly in the eastern than in 
the western quarter when the sun is in the east. This is due to two causes: 
the first is that the sun shines with its rays through the particles of the 
smoke, and lightens these up and renders them visible; the second is 
that the roofs of the houses seen in the east at this hour are in shadow, 
because their slope prevents them from being lighted by the sun; the 
same happens with the dust, and both the one and the other are more 
charged with light in proportion as they are thicker; and they are 
thickest towards the middle. g22 v 


When the sun is in the east the smoke of cities will not be visible in 
the west, because it is neither seen penetrated by the solar rays nor 
against a dark background, since the roofs of the houses turn the same 
side to the eye that they show to the sun, and against this bright back- 
ground the smoke will be scarcely visible. But dust when seen under 
the same conditions will appear darker than smoke, because it is thicker 
in substance than smoke, which is made up of vapour. ^ ^ 

\Of trees penetrated by the air] 


The intervening region of the air within the bodies of trees, and the 
spaces between the trees within the air at a great distance, do not reveal 
themselves to the eye, for where it requires an effort to discern the whole 
it would be difficult to distinguish the parts. But it forms a confused 
mixture, which derives most from that which forms the greatest mass. 
The open spaces of the tree being made up of particles of illuminated 
air, and being much less than the tree, one therefore loses sight of them 
much sooner than one does of the tree; but it does not therefore follow 
that they are not there. Hence of necessity there comes about a blending 
of air and of the darkness of the shaded tree, which float together to 
meet the eye of the beholder. 

O N E A N O T H E R ^ ^ ^ ^ ^ ^ ^ 

That part of the tree will show fewer open spaces when it has behind 
it, between the tree and the air, the greater mass of another tree. So with 

312 . ■ ■ ■ . ■ . ■ ■ 


the tree a the open spaces are not covered, nor in ^ because there are no 
trees behind. But in c there is only open space in the half, that is to 
say that c is covered by the tree c/, and part of the tree d is covered by the 
tree and a little beyond this all the open spaces within the circum- 
ference of the trees are lost, and only those at the sides remain. 

■' G 2C V. 


What outlines do trees show at a distance against the atmosphere 
which serves as their background? The outlines of the structure of trees 
against the luminous atmosphere, as they are more remote, approach the 
spherical more closely in their shape, and as they are nearer, so they 
display a greater divergence from the spherical form. 

So the first tree a'^ as being near to the eye displays the true form of 
its ramification, but this is somewhat less visible in and disappears 
altogether in where not only can none of the branches of the tree be 
seen, but the whole tree can only be recognised with great difficulty. 

Every object in shadow — be it of whatever shape you please — will 
at a great distance appear to be spherical; and this occurs because if an 
object be rectangular, then at a very short distance its angles become 
invisible, and a little farther off it loses more than it retains of the lesser 
sides, and so before losing the whole it loses the parts, since these are 
less than the whole. 

So with a man when so situated, you lose sight of the legs, arms and 
head, before the trunk, and then the extremities of the length become 
lost before those of the breadth, and when these have become equal 
there would be a square® if the angles remained, but as they are lost 
there is a sphere. g 26 v 

In the representation of trees in leaf be careful not to repeat the 
same colour too often, for a tree which has another tree of the same 
colour as its background, but vary it by making the foliage lighter or 
darker, or of a more vivid green. G27V. 

^ MS- contains a sketch of a row of trees seen in perspective. 

® I have followed Dr. Richter in interpreting a tiny figure in the text as a square. 
M. Ravaisson-Mollien reads it as d. 

.313 , ■ ■ 



The lights on such leaves as are darkest in colour will most closely 
resemble the colour of the atmosphere reflected in them; and this is due 
to the fact that the brightness of the illuminated part mingling with the 
darkness forms of itself a blue colour; and this brightness proceeds from 
the blue of the atmosphere, which is reflected in the smooth surface of 
these leaves, thereby adding to the blueness which this light usually 
produces when it falls upon dark objects. 


But leaves of yellowish green do not when they reflect the atmosphere 
create a reflection which verges on blue; for every object when seen in a 
mirror takes in part the colour of this mirror; therefore the blue of the 
atmosphere reflected in the yellow of the leaf appears green, because 
blue and yellow mixed together form a most brilliant green, and there- 
fore the lustre on light leaves which are yellowish in colour will be a 
greenish yellow. 


The trees, illuminated by the sun and by the atmosphere, which 
have leaves of a dark colour, will be illuminated on one side by the 
atmosphere alone, and in consequence of being thus illuminated will 
share its blueness; and on the opposite side they will be illuminated 
both by the atmosphere and the sun, and the part which the eye sees 
illuminated by the sun will be resplendent. g28v 

The extremities of the branches of trees if not dragged down by the 
weight of their fruit turn towards the sky as much as possible. 

The upper sides of their leaves are turned towards the sky in order 
to receive nourishment from the dew that falls by night. 

The sun gives spirit and life to plants, and the earth nourishes them 
with moisture. In this connection I once made the experiment of 
leaving only one small root on a gourd and keeping this nourished with 
water; and the gourd brought to perfection all the fruits that it could 
produce, which were about sixty gourds of the long species; and I set 
myself diligently to consider the source of its life, and I perceived that 
it was the dew of the night which steeped it abundantly with its moisture 
■ ■ 314 ■ 


through the joints of its great leaves, and thereby nourished the tree 
and its offspring, or rather the seeds which were to produce its offspring. 

The rule as to the leaves produced on the last of the year’s branches 
is that on twin branches they will grow in a contrary direction, that is, 
that the leaves in their earliest growth turn themselves round towards 
the branch, in such a way that the sixth leaf above grows over the sixth 
leaf below; and the manner of their turning is that if one turns towards 
its fellow on the right, the other turns to the left. * 

The leaf serves as a breast to nourish the branch or fruit which grows 
in the succeeding year. 

° G 32 V. 


The dark colours of the shadows of mountains at a great distance 
take a more beautiful and purer blue than those parts which are in light, 
and from this it follows that when the rock of the mountains is reddish 
the parts of it which are in light are fawn-coloured, and the more 
brightly it is illuminated the more closely will it retain its natural 
colour. Q 


Smoke enters into the air in the form of a wave, like that which 
water makes when its force causes it to burst through other water. 

I 106 [58] r. „ 

Reeds in the light are scarcely visible, but between the light and 
the shade they stand out well. 

To represent landscapes, choose when the sun is at the meridian 
and turn to the west or the east, and then begin your work. 

If you turn to the north every object placed on that side will be 
without shadow, and especially those nearest to the shadow cast by your 
head, and if you turn to the south every object’ upon that side will be 



Low, tall, thin, thick, that is with leaves, dark, light, yellow, red, 
with branches pointing upwards, with branches that meet the eye, with 
branches that point downwards, with trunks white, those transparent in 
the air, those not, those massed together, those spread out. i, 87 v 

The line of equality and that of the horizon are the same. ^ ^ 

Landscapes are of a more beautiful azure when in fine weather the 
sun is at noon, than at any other hour of the day, because the atmosphere 
is free from moisture; and viewing them under such conditions you see 
the trees beautiful towards their extremities and the shadows dark 
towards the centre; and in the farther distance the atmosphere which is 
interposed between you and them appears more beautiful when beyond 
it there is some darker substance, and consequently the azure is most 

Objects seen from the side on which the sun is shining will not show 
you their shadows. But if you are lower than the sun you will see what 
was not seen by the sun, and that will be all in shadow. 

The leaves of the trees which are between you and the sun are of 
five principal shades of colour, namely a green most beautiful, shining and 
serving as a mirror for the atmosphere which lights up obj ects that cannot 
be seen by the sun, and the parts in shadow that only face the earth, and 
those darkest partswhicharesurroundedbysomethingotherthandarkness. 

Trees in the open country which are between you and the sun seem 
much more beautiful than those which have you between the sun and 
themselves; and this is the case because those which are in the same 
direction as the sun show their leaves transparent towards their 
extremities, and the parts that are not transparent, that is at the tips, are 
shining; it is true that the shadows are dark, because they are not covered 
by anything. 

The trees when you place yourself between them and the sun will 
only show themselves to you in their clear and natural colour, which is 
not of itself very conspicuous, and besides this certain reflected lights, 
which, owing to their not being against a background that offers a 
strong contrast to their brightness, are but little in evidence; and if 
you are at a lower altitude than these, such parts of them may be visible 
as are not exposed to the sun, and these will be dark. 



But if you are on the side from whence the wind is blowing, you will 
see the trees looking much lighter than you would see them from 
the other sides; and this is due to the fact that the mnd turns up the 
reverse sides of the leaves, which are in all cases much paler than their 
right sides; and especially will they be very light if the wind blows from 
the quarter where the sun happens to be, and if you have your back 
turned to it. b.m. 113V. 

All trees seen against the sun are dark towards the centre; this 
darkness will take the shape of the tree when it stands apart from others. 
The shadows cast by trees on which the sun is shining are as dark 

as that of the centre of the tree. 

The shadow cast by trees is never less in mass than the mass of th 
tree; hut it is larger in proportion as the place where it is thrown slopes 

more towards the centre of the earth. 

A shadow will be thickest towards the centre of a tree when it has 

^*'^Ever 7 branch gets the middle of the shadow of every other branch 

and as a consequence of all the tree. . 1 1 j -..-u 

The shape of every shadowof branch or tree is clothed with f^ bngh^ 
part on the side from which the light comes; this brightness wdl be of 
the same shape as the shadow and may extend for a mile from the side 

where the sun is. , , 

If it should happen anywhere that a cloud casts a shadow on som 
part of the hills, the trees there will undergo less change than in the 
distances or plains; for the trees upon the hills have their tr“^ 
thicker because their growth each year is less than in the 
as they are of the number of those naturally dark and full of shade the 
shadows of the clouds cannot make them any darker, and the levd 
spaces that come between the trees which have not lost any shadow 
vary very much in tone, and especially those which are o*er than green, 
such as cultivated lands or the havoc of mountains or their barrenness or 

"“^mere wees are on the skyline they seem of the sarne colour, unless 
they are very close together and with thick-set leaves like the pine and 

'“when you see trees on the side on which the sun lighn them you will 



see them of almost uniform brightness, and the shadows which are within 
them will be covered by the illuminated leaves which come between 
your eye and the shadows. 

When trees come between the sun and the eye beyond the shadows 
which spread out from their centre you will see the green of the leaves 
in transparence; but this transparence will be broken in many places 
by the leaves and branches in shadow which come between you and them, 
and in the upper portions it will be accompanied by many reflections 
from the leaves. 

B.M. 1 14 r. 

When the sun is covered by clouds, objects have a low degree of 
visibility; because there is but little difference between the lights and 
shadows of the trees and buildings, through them being illuminated by 
the spaciousness of the atmosphere, which surrounds the objects in such 
a way that the shadows are few, and these few become fainter and fainter 
so that their extremities become lost in mist. 

The trees in landscapes are of various different shades of green; for 
in some, such as firs, pines, cypresses, laurels, box and the like, it borders 
on black; others such as walnuts and pears, vines and young foliage 
approximate to yellow; others to darker shades of yellow, such as chestnuts, 
oaks and the like, others redden towards the autumn, these are sorbs, 
pomegranates, vines and cherry trees; others such as willows, olives, 
bamboos, and others like these, tend to become white. 

B.M. 1 14 V. 


All the leaves which hang down towards the ground as the twigs 
bend, owing to the branches being turned over, straighten themselves 
in the current of the winds; and here their perspective is inverted, for if 
the tree is between you and the quarter from which the wind is coming, 
the tips of the leaves which are towards you take their natural position, 
and those opposite which should have their tips the contrary way, from 
the fact of their being upside down, will be turned with their tips towards 

Trees in a landscape do not stand out distinctly one from another, 
because their illuminated parts border on the illuminated parts of those 


: beyond them, and so there is little difference between the lights and 

the shadows. 

i When clouds come between the sun and the eye all the edges of their 

I rounded masses are clear, and they are dark towards the centre, and this 

* happens because towards the top these edges are seen by the sun from 

above while you are looking at them from below; and the same happens 
I with the positions of the branches of the trees; and moreover the clouds, 

like the trees, through being somewhat transparent are partly bright, and 
at the edges show themselves thinner. 

But when the eye finds itself between the cloud and the sun, the 
appearance of the cloud is the contrary of what it was before, for the edges 
of its rounded masses are dark and they are bright towards the centre. And 
r this comes about because you are looking at that part which is also facing 

I the sun, and because these edges have a degree of transparency and reveal 

I to the eye the part that is hidden beyond them, and this not being visible 

, to the sun as are the parts which are turned towards it is necessarily 

i somewhat darker. It may also be that you see the details of these 

rounded masses from the under side while the sun sees it from above, 
and since they are not so situated as to give back the brightness of the 
sun as in the former instance, therefore they remain dark. 

The black clouds which are often visible above those that are bright 
f and illuminated by the sun, are thrown into shadow by the other clouds 

which are interposed between them and the sun. 

Again the rounded masses of the clouds that face the sun show their 

i edges dark, because they are silhouetted^ against a bright background; 

and to see the truth of this you should observe the top of a cloud which 
is entirely light because it is silhouetted against the blue of the 
atmosphere which is darker than the cloud. 

•f B.M. 172 V. 

O F M o V E M E N T 

I ask whether the true movement of the clouds can be recognised 
by the movement of their shadows, and similarly by the movement of 
the sun. -c. * ' . 

Forster ii 46 r. 

The sun will appear greater in moving water or when the surface is 
broken into waves than it does in still water. An example is of the 
light reflected on the strings of themonochord. 

^ MS. caftpegiano. 

, . ■ ■ ■■ 319- ■ ■ 


O V E N O R B U R N I N G K I L N 

The clouds do not display their roundnesses except in those parts 
which are seen by the sun: other roundnesses are imperceptible because 
they are in the parts in shadow. 

If the sun is in the east and the clouds are in the west, the position 
of the eye being between the sun and the cloud, it sees the edges of the 
roundnesses which are the component parts of these clouds as dark, and 
the portions which are surrounded by these darknesses become light. 
And this proceeds from the fact that the edges of the rounded forms of 
these clouds face the sky above and around them, so that it is mirrored 
in them. 

The cloud and the tree display no roundness in those of their parts 
wMcll arein shadow. Windsor: Drawings 1^388 

The shadows of clouds are lighter in proportion as they are nearer 
to the horizon. • 

Windsor: Drawings 12391 

That part of a tree which is against a background of shadow is all 
of one tone, and where the trees or branches are thickest there it is 
darkest because there is less perforation by the air. But where the 
branches are on a background of other branches there the luminous 
parts show themselves brighter and the leaves more resplendent, because 
of the sun which illumines them. - 

Windsor; Drawings 1243 1 V. 

P A I N T I N G 

The density of smoke below the horizon appears white and above 
the horizon dark, and even though the smoke is in itself of uniform 
colour this uniformity will seem to vary, according to the difference 
of the space in which it is found. ; 

^ Windsor MSS. R 878 


Light and Shade 

‘No substance can be comprehended without 
light and shade; light and shade are caused by 

That place is most shaded on which the greatest number of shaded 
rays converge. 

That place which is smitten by the shaded rays at the greatest angle 
is darkest. 

That place will be most luminous from which the greatest number of 
luminous rays are reflected. 

•' C.A. 3 1 V. b 

Light is the expeller of darkness. Shadow is the suppression of 

Primary light is that which is the cause of the lighting of shaded 

And the derived lights are those parts of bodies which are illumined 
by the primary light. 

Primary shadow is that side of a body on which the light does not 


Derived shadow is simply the striking of shaded rays. 

Each body which creates a concourse of rays fills the surrounding 
air with an infinite number of its images. 

A shaded and luminous concourse is that mass of rays which 
emanate from a shaded and luminous body running through the air 
without striking. 

Shaded or luminous percussion is that which impedes and cuts 
above itself the concourse of shaded and luminous rays. . , 

•' c.A. no r. b 

The shadow in diaphanous and spherical bodies is darker at the top 
than in the hollow, and darker amid the darkness of the derived shadow 
of the body of the ball. 

Every object seen is surrounded by second objects, and from this it 
is known: and in proportion as the second object is farther away than 
the first so much the more does the first cover it from the eye. 

C.A. 125 r. b 

Among the things of equal obscurity which are situated at a con- 
siderable and equal distance, that will appear more obscure which has 
its station higher up from the earth. 

The edges of a derived shadow will be most distinct where it is cast 
nearest to the original shadow. 

A shaded body will appear of less size when it is surrounded by a very 



luminous background, and a luminous body will show itself greater 
when it is set against a darker background: as is shown in the heights of 
buildings at night when there are flashes of lightning behind them. For 
it instantly appears, as the lightning flashes, that the building loses a part 
of its height. 

And from this it comes to pass that these buildings appear larger 
when there is mist, or by night, than when the air is clear and illumined. 

C.A. 126 r. b 

The breadth and length of shadow and of light, although through 
foreshortening it may appear less in quantity, will not therefore appear 
diminished as to quality either in respect of brightness or darkness. 

C.A, 144 V. a 

All the illuminated parts of a body which see the whole circle of the 
luminous body will be the more dissimilar in brightness, one from 
another, as they are nearer to the source of the light. c a i co r a 

T'he atmosphere is of itself adapted to gather up instantaneously and 
to leave behind it every image and likeness of whatever body it sees. 

When the sun appears in the eastern horizon it permeates at once the 
whole of our hemisphere and fills it with its luminous semblance. 

All the surfaces of solid bodies turned towards the sun or towards 

the atmosphere illumined by the sun, become clothed and dyed by the 
light of the atmosphere or of the sun. 

Every solid body is surrounded and clothed with light and darkness. 

You will get only a poor perception of the detail of a body when the 
part visible is all the part in shadow, or only the part that is illumined. 

The length of the space which exists between the eye and the solid 
bodies determines how much the part that is illumined increases, and that 

in shadow diminishes. 

The shape of a body cannot be accurately perceived when its 
extremities are bounded by something of the same colour as itself, and 
the eye is between the part in shadow and that in light. ^ ^ ^ ^ 

No separated shadow can reproduce upon a wall the true form of the 
body of which it is the shadow, unless the centre of the light is equidistant 
from the extremities of this body. „ 

■' C.A. 187 V. a 



[Camera Obscurd\ i 

The boundaries of the images of any colour which penetrate through 1 

a narrow hole into a dark place will be always of a more powerful colour ; 

than its centre. , - 

C.A. 190 r. b ^ 

Why black painted in juxtaposition with white never seems to show s 

itself more black than where it borders upon black, and white does not ‘ 

show itself more white in juxtaposition with black than with white; as 
is seen with the images passed through a hole or at the edge of any dark 
obstacle. | 

This comes about because the images tinge with their colour the ! 

spot on which they fall, and when the different images approach the ' 

same spot they make a blend of their colours, and this blend participates 
more in one colour than in another as the one colour is present in 5 

greater quantity than the other. I 

And the colours are more intense and more sharply defined at their | 

edges than in any other part. ^ , . j 



Those who have experience use in all intricate things such as trees, j 

meadows, hair, beards and fur, four stages of clearness in order to \ 

reproduce the same colour; that is, first a dark foundation, second a blur j 

which has something of the shape of the part, third a clearer and more j 

defined part, fourth the lights more in high parts for movements of the | 

figure it seems however to me that these varieties are infinite in the [ 

case of a continuous quantity, which is in itself divisible to infinity, and 
thus I prove it: 1 

[Two diagrams] J 

Let a ght 2. continuous quantity and d the light that illumines it. 

I refer now to the fourth which says that that part of the illuminated 

body will be more luminous which is nearer to the source of its illumina- i 

tion; g therefore is darker than c in proportion as the line d g\s> longer 

than the line d c. And from the conclusion that such grades of bright- ‘ 

ness, or if you so prefer of darkness, are not four only, but may be > 

conceived of as infinite, because ^ is a continuous quantity, and every I 

continuous quantity is divisible to infinity, therefore the variety in the I 

^ ilumi pitl che alte parte moti di figura i 



length of the lines that extend from the luminous to the illuminated body 
is infinite; and the proportion of the lights corresponds to the lengths of 
the lines between them, which extend from the centre of the luminous 
body to the part of the object which is illuminated by it. c a 199 v a 


If the whole light were what caused the shadows behind the bodies 
placed against it, it would be necessary that that body, which is much 
less than the light, should have a pyramidal shadow behind itself, and as 
experience does not confirm this, it must be that it is the centre of the 
light which performs this function. 


The cannon-ball from the mortar, if it be of uniform substance, and 
its surface be equidistant from its centre, and the fire strikes it in the 
middle, as reason would suggest, must needs take its course without any 
revolution. Seeing that the fire that expels it is of uniform nature, it 
drives equally the air which withstands its course, and as this also is 
equal it offers equal resistance, 


Thus for example, one sees the moon, which is also a spherical body 
and meets with equal resistance, to be much swifter as compared with 
the cannon-ball, but nevertheless the dark spots that are on it never 
change their position, and the fact of this change not appearing, clearly 
confirms the fact that it does not revolve. 


If you look at the sun or other luminous object and then shut your 
eyes, you will see it again in the same form within your eye for a long 
space of time: this is a sign that the images enter within it. ^ ^ 

When the intersection of two columns of shadow produces their 
derived shadows by means of the two luminous ones, it must follow that 
four derived shadows are produced, and these shadows are composite, 
and they intersect at four places ; and of these intersections there are two 
that form simple shadow, and two are of composite shadow, and these 

■ 326 , . 


two simple shadows are produced where the two lights cannot be seen, 
and the composite shadows are produced where one of the two lights 
cannot illumine. But the intersections of the composite shadows are 
produced always by a single luminous body, and of the simple ones by 
two luminous bodies, and the right intersection of the composite shadow 
is produced by the left light, and the left intersection is produced by the 
right light; but the two intersections of the simple shadows, both the 
upper and the lower, are produced by the two luminous bodies, that is 
the light on the right and the light on the left. c a 241 r c 

Many minute lustres continue in the far distance and make them- 
selves perceptible. 


With reference to the light that penetrates the vent holes, it may be 
doubted whether it reconstitutes with the dilatation of its rays as much 
breadth of impression beyond the vent hole as the width of the body 
which is the cause of the rays. 

And in addition to this, whether this dilatation has a power equal to 
that of the luminous body. As regards the first doubt the reply is that 
the dilatation made by the rays after their intersection recreates as much 
breadth beyond the vent hole as in front of the vent hole, there being as 
much space from the luminous body to the vent hole as from the vent 
hole to the impress of its rays; this is proved by the straightness of the 
luminous rays, from which it follows that there is the same propor- 
tion between their breadth and between the distances at which they 

But power does not proceed in the same proportion; as is proved 
where it is stated: just such proportion exists between the heat and the 
radiance in the different luminous rays as between their distances from 
their source. It is proved therefore that the luminous ray loses in heat 
and radiance in proportion as it is more remote from its luminous body. 
It is true however that the composite shadows, being derived, and 
starting from the edges of these vent holes, break this rule by means of 
their intersections; and this is treated of fuUy in the second book 
concerning shadow. c.A.24ir.d 


The rays of the shaded and luminous images intersect after they 
have penetrated within the vent holes, turning in opposite directions 
every part of their thickness. 

C.A. 241 V. C 

The shadow will never show itself of uniform density in the place of 
its incidence, unless this place be equidistant from the luminous body. 
This is proved by the seventh which says: that shadow will show itself 
lighter or darker which is against a darker or lighter background; by 
the eighth of this: that background will have its parts so much darker or 
lighter as it is more remote from or nearer to the luminous body; and 
among the positions at an equal distance from the luminous body that 
will show itself more illuminated which receives the luminous rays at 
more equal angles. No matter with what inequality of position a 
shadow is defined, it will always show itself with its true boundaries equal 
to the shaded body if the eye rests upon the centre of the luminous body. 

That shadow will show itself darker that is more remote from its 
shaded body. 

■" C.A. 241 V. d 

The image of the sun is all in all the parts of the objects upon which 
its rays fall, and all in each particular part. 

Why in the far distance a radiance which is long will appear round to 
us, and the horns of the moon do not follow this rule, and yet the light 
near by follows as its point indicates. 

C.A. 243 r. a 


Having, as I think, sufficiently treated of the natures and different 
characteristics of primary and derived shadows, and the manner of their 
incidence, it seems to me that the time has now come to explain the 
different results upon the various surfaces which are touched by these 


It seems to me that the shadows are of supreme importance in 
perspective, seeing that without them opaque and solid bodies will be 
indistinct, both as to what lies within their boundaries and also as to 
their boundaries themselves, unless these are seen against a background 
differing in colour from that of the substance; and consequently in the 
first proposition I treat of shadows, and say in this connection that 



every opaque body is surrounded and has its surface clothed with 
shadows and lights, and to this I devote the first book. Moreover these 
shadows are in themselves of varying degrees of darkness, because they 
have been abandoned by a varying quantity of luminous rays; and 
these I call primary shadows, because they are the first shadows and so 
form a covering to the bodies to which they attach themselves, and to 
this I shall devote the second book. From these primary shadows there 
issue certain dark rays, which are diffused throughout the air and 
vary in intensity according to the varieties of the primary shadows from 
which they are derived; and consequently I call these shadows derived 
shadows, because they have their origin in other shadows; and of this I 
will make the third book. Moreover these derived shadows in striking 
upon anything create as many different effects as are the different 
places where they strike; and of this I will make the fourth book. And 
since where the derived shadow strikes, it is always surrounded by the 
striking of the luminous rays, it leaps back with these in a reflex stream 
towards its source and meets the primary shadow, and mingles with 
and becomes changed into it, altering thereby somewhat of its nature; 
and to this I will devote the fifth book. In addition to this I will make 
the sixth book to contain an investigation of the many different varieties 
of the rebound of the reflected rays, which will modify the primary 
shadow by as many different colours as there are different points from 
whence these luminous reflected rays proceed. Further I will make the 
seventh division treat of the various distances that may exist between the 
point of striking of each reflected ray and the point from whence it 
proceeds, and of the various different shades of colour which it acquires 
in striking against opaque bodies. ca ^sor a 

In proportion as the luminous body is nearer to the shaded body, it 
throws out more light if the luminous body is greater than the dark body. 

In proportion as the luminous body is more distant from the shaded 
body and is less than it, it will give more light. 

But in proportion as the luminous body being less than the shaded 
body is more distant from this shaded body it will give more light. 

And if the luminous body being greater than the shaded body is 
moved farther away from the shaded body, the total amount that is 
illuminated will continue to diminish until it is approximately half. 


T H E A C T I O N O F C O M P O U N D S H A D O W 

The actions of compound shadows are always made up of contrary 
movements. That is, that if the concourse of luminous rays before 
arriving at their point of intersection be touched by an opaque body, all 
the shadows of that body which breaks in upon the upper ray will show 
themselves beyond this point of intersection in the percussion of the 
lower ray, and as the upper ray becomes the lower after the intersection, 
so the movements which the shaded body makes within this upper ray 
will show themselves of contrary movement after this intersection; and 
this will reveal itself in the incidence of the compound shadow upon the 
pavement, or on a wall that is struck by the sun or other luminous body. 

But if the luminous ray is interrupted by the opaque body some 
distance from its intersection, the percussion of the derived shadow of the 
opaque body will make a movement similar to that of the opaque body. 

And if these rays are interrupted at the actual point of their inter- 
section, then the shadows of the opaque body will be twofold, and they 
will move with contrary movements one to another before they reach 
the point of union. 

The derived compound shadow is the cause why the percussion of 
the solar ray when passing through any kind of angle does not leave its 
impression on this angle; but portions of. . .so much greater or less . . , 
in proportion as these impressions are more remote from or nearer to 
these angles. 

° ' C.A. 277 V. a 

The site that is most luminous will vary according to the different 
positions of the eye and the light; and the shadow will always be im- 
movable, for whatever the change it makes, the eye sees it. ^ ^ ^ ^ 

No opaque body can be visible unless it is clothed with a shaded and 
illuminated surface. 

The air and every transparent body becomes a passage from the 
objects to the eye for the images of those bodies which find themselves 
either within or beyond them. 

Derived light should be surrounded by primitive shadow. 

Derived shadow will be surrounded by derived light. 

Derived light should be surrounded, in whole or in part, by primitive 
or derived shadows. 


Every opaque body has its image all in all and all in every part of 
the transparence that surrounds it. , 

C.A. 349 V. d 

O F P A I N T I N G 

Of the shadows — where they ought to be dark; where the shadows 
ought to be of a middle degree, and the lights where they ought to be 

Where they are darker. Where there ought to be glimmers and 
reflections, that is lights thrown back in one place, and leaping up again 
in another. 

How lights ought to be so rendered that they draw natural things. 

How natural figures when they have intense light on one side seem 
to be in the deepest shadow on the opposite side. 

How men show a small variation from light to shadow when the 
atmosphere is overcast or the sun is on the point of setting. 

For what reason objects as they recede from the eye are perceived 
poorly and seem to lose clearness of outline, and in the far distance appear 

Why things when painted seem greater than they are. ^ ^ ^ ^ 

That light is brightest which has the greatest angle. 

That shadow is darkest which is produced at a most acute angle. 

C.A. 385 V. C 

Primary and derived shadow are deeper when they are caused by 
the light of the candle than by that of the atmosphere. 

The more the derived shadow which is greater enters in the less, the 
more the cause of the less is more luminous than the greater. 

Tr. 24 a 

The edges of the window which are illuminated by two different 
lights of equal radiance will not throw light of equal quality into the 
room. Tr.2Sa 

\Wtth sketcK\ 

At the window a b the sun enters into the house; this sun will increase 
the size of the window and lessen the shadow of a man, with the result 
that when the said man shall approach this shadow of himself, lost in that 
which carries the true shape of the window, he will see the contact of the 

■331 : 


shadows lost and confused by the power of the light, close themselves up 
and not suffer the solar rays to pass ... 

And the shadow made by the man upon the said contact has pre- 
cisely the effect that is represented above. 

]With diagram\ 

If you wish to measure a height by the shadow of the sun, take a stick 
which may be one braccio, set it up and wait until the sun makes it cast 
a shadow of two braccia. Then measure immediately the shadow of the 
tower, and if this is one hundred braccia the tower will be fifty; and this 
is a good rule. 

1 6 r. 

That part of a shaded body which is illuminated will transmit to the 
eye the image of its details more distinctly and more rapidly than that 
which finds itself in shadow. 


Among bodies equal in size and distance that which shines the more 
brightly seems to the eye nearer and larger. 

The straight edges of bodies will appear broken when they serve as 
boundary of a dark space streaked by the percussion of luminous rays. 

The body illuminated by the solar rays which have passed through 
the thick branches of the trees, will cast as many shadows as is the number 
of the branches interposed between the sun and itself. 

The shaded rays which proceed from a pyramidal shaded body will 
bifurcate when they intersect, and the shadow will be of varying degrees 
of depth at its points. 

A light which is greater than the point and less than the base of the 
shaded pyramidal body placed in front of it, will cause the shaded body to 
produce at its percussion a bifurcated shadow of varying degrees of depth. 

If a shaded body being smaller than a luminous body casts two 
shadows, and a shaded body the same size as a luminous body or greater 
than it casts one, it follows that the pyramidal body of which part is 
smaller than, part equal to, and part larger than the luminous body, will 
cast a bifurcated shadow. 



The body that receives the solar rays which have passed between the 
minute ramifications of trees at a great distance will have but a single 

If the body, part in shadow and part in light, be of the shape ot a per- 
fect sphere, the base of the luminous pyramid will bear the same propor- 
tion to its body as that which the base of the shaded pyramid bears to the 

shaded body. . _ 

In proportion as the percussion made by the convergence or tne 
shadow on the opposite wall is more distant from the luminous body and 
nearer the source from which it is derived, so much the darker and of 

more defined contours will it appear. cav. 

That luminous body will appear of less radiance which is surrounded 

by a more luminous background: 

I have found that those stars that are nearest the horizon appear 
larger in form than the others, because they see and are seen by a greater 
amount of the solar body than when they are above us; and since they 
see more of the sun they have a greater light. And the body that is most 
luminous shows itself of greater form, as the sun shows itself in the mist 
above us, for it seems larger when it is without mist and with the mist it 

No part of the luminous body is ever visible from the pyramid of 
pure derived shadow. c3r. 

[Movement of shadows\ ^ ■. j j u 

If the object is moved slowly before the luminous body and the per- 
cussion of the shadow of this object is remote from its object, the 
movement of the derived shadow will have the same proportion with the 
movement of the primary, as the space between the object and the light 
has with that between the object and the percussion of the shadow, - so 
that when the object moves slowly the shadow is rapid. c 3 v. 

That part of the reflection will be brightest in which the reflected 

rays are shortest. ^ , . 

The darkness caused by a number of shadows intersecting will be in 
conformity with their cause, which has its beginning and end between 
smooth surfaces near to each other, of the same quahty and directly 
Opposite to each other. 



In proportion as the luminous body is greater the course of the 
luminous and shadow rays will be more mingled together. 

This comes about because where the larger number of luminous rays 
are found, there is most light, and where a lesser number, less light, from 
which it comes about that the shadow rays enter and mingle with them. 

c 4 r. 

That part of the surface of bodies on which the images of the bodies 
placed opposite, fall at the largest angle will be tinged most with their 

The most luminous part of the illuminated body which encompasses 
the percussion of the shadow will be that which is nearest to this per- 

Just as a thing touched by a greater mass of luminous rays becomes 
brighter, so that will become darker which is struck by a greater mass of 
shadow rays. 

■' c 4 V. 

A luminous body will seem more brilliant when it is surrounded by 
deeper shadow. 

The breadth and length of shadow and light, although through fore- 
shortening they become straighter and shorter, will neither diminish nor 
increase the quality or quantity of their brightness or darkness. 

The function of shadow and of light diminished by foreshortening, 
will be to shade and illumine an object opposite to it, according to the 
quality and quantity that appear in this object. 

The more a derived shadow approaches its penultimate extremities 
the deeper it will appear. ^ ^ ^ 


If you cause the rays of the sun to pass through a small hole of the 
shape of a star you will see beautiful effects of perspective in the per- 
cussion caused by the passage of the sun. ^ ^ ^ 


The forms of shadows are three: for if the substance which casts the 
shadow is equal in size to the light, the shadow is like a column which 
has no end; if the substance is greater than the light, its shadow is like a 
pyramid which grows larger as it recedes and of which the length has 


no end; but if the substance is smaller than the light the shadow resembles 
a pyramid and comes to an end, as is seen in the eclipses of the moon. 

c 7 V. 

O F L I G H T 

The shape of a luminous body although it has length will at a great 
distance seem round. 

This is shown by the flame of the candle, which although it is long 
seems round at a great distance; and the same thing may happen with 
the stars, for even if they were horned like the moon they would seem 
round by reason of their great distance. c 8 r 

Among bodies equal in size and length and equal also in form and 
depth of shade, that will appear the smaller which is surrounded by a 
more luminous background. 

A shaded body placed between equal lights will cast as many shadows 
as there are lights, shadows of which one will be darker than the others 
as the light situated on the opposite side is nearer this body than the 

A shaded body equidistant between two lights will cast two shadows, 
one darker than the other in proportion as one of the lights which cause 
them is greater than the other, c 8 v 

The places occupied by the shadows caused by a small luminous body 
are, as regards size, similar and corresponding to those of which the visual 
rays are cut off. 

And when the luminous ray has passed through a small hole and 
been broken upon some opposing object near at hand, the impress of its 
percussion resembles more the hole through which it has passed than the 
luminous body from which it proceeds. C9r 

The greater the radiance of the luminous body the deeper will be 
the shadows cast by the bodies it illuminates. 

All the shaded bodies that are larger than the pupil, which interpose 
between the eye and the luminous body, will show themselves dark. 

If the eye be placed between the luminous body and the bodies 
illuminated by this light, it will see these bodies without any shadow. 

■ , c lo r. . 

When a luminous ray has passed through a hole of some unusual 


shape after a long course, the impression it makes where it strikes 
resembles the luminous body from which it springs. 

It is impossible for the ray born of a luminous spherical body to be 
able, after a long course, to convey to where it strikes the image of any 
description of angle that exists in the angular hole through which it 

^ C lO V. 

The shape of the derived shadow will always conform to the shape of 
the original shadow, 

A light in the form of a cross thrown on to a shaded body of spherical 
roundness will produce its shadow in the figure of a cross. ^ ^ ^ ^ 

That boundary of the derived shadow is darker which is surrounded 
by a brighter derived light. ^ ^ 

Of things equal in respect of size, brightness, background and 
length, that which has the smoothest surface will seem largest. 

Iron of uniform thickness half of which is heated serves as a proof, 
for the part that is heated appears larger than the remainder. 

[Of broken shadowl 

The derived shadow which has as its origin and cause a spherical 
shaded and luminous body, and is broken by the percussion made by it 
upon different bodies situated at varying degrees of distance, will appear 
round to the eye that is in front of it situated near to the centre of the 
original shadow. 

A shaded body of spherical rotundity will cast a circular shadow 
blended [of light and shade] when it has a shaded body of its own sub- 
stance interposed between it and the sun. 

^ C T V. 

Among shadows of equal quality that nearest the eye will appear 
least dark. 

That shadow will be darker which is derived from a greater number 
of different shaded and luminous bodies. 

It is impossible that simple derived shadows, which spring from dif- 
ferent bodies and are caused by a single light, can ever join or touch each 

C 13 V. 


\When adjacent bodies mil appear separated?^ 

If many shaded bodies, so near to each other as to be almost touch- 
ing, are seen against a luminous background at a great distance, they 
will seem separated by a great space. ^ ^ 

[When separated bodies will appear adjaceni\ 

If many luminous bodies are seen in a distant landscape, although 
they may be separated one from another, they will appear united and 
joined together. 

That part of the air will participate most in its natural darkness 
which is smitten by the sharpest luminous angle. It is clearly to be 
understood that where there is a smaller luminous angle there is less 
light, because the pyramid of this angle has a smaller base, and there- 
fore from this smaller base a lesser number of luminous rays converge at 
its point. 


Darkness is the absence of light. 

Shadow is the diminution of light. 

Primitive shadow is that which is attached to shaded bodies. 

Derived shadow is that which separates itself from shaded bodies and 
travels through the air. 

Repercussed shadow is that which is surrounded by an illuminated 

The. simple shadow is that which does not see any part of the light 
which causes it. 

The simple shadow commences in the line which parts it from the 
boundaries of the luminous bodies. 

c 14 V. 

Rays doubled by intersection in lights and shadows are also of 
double clearness or obscurity: 

Primitive light and derived reflected light, when they surround thick 
and spherical bodies, become the cause of the boundaries of the primitive 
shadows of these bodies, being so much more distinct and defined in the 
part near to the lights, as the derived light is clearer than the primitive. 

That is said to be primitive light which first lights up shaded bodies, 
and that is called derived which leaps back from these bodies in those 
parts which are remote from this primitive light. 


That part of the primitive shadow will be more luminous which can 
see more equally the centres of the derived lights. 

One may clearly know that that part of the shaded bodies which is 
seen by a greater quantity is the more luminous, and especially if it is 
illumined by two lights; as is seen with reflected lights which put in their 
midst the derived shadow made between them by the dense bodies 

Every luminous body illumines with its whole and with its part the 
part and the whole of the object turned to face it. 

This proposition is very evident, for one cannot deny that where the 
whole pupil of the eye is looking, there every part of it is looking, and 
the place seen by this pupil acts in the same way towards it. c i6 v 

The middle of the length of each derived shadow is in a straight line 
with the middle of the primitive shadow and of the derived light, and the 
centres of the shaded and luminous bodies. 

This necessarily happens, since as the luminous lines are straight, 
those which pass by the extremities of the shaded bodies enclose within 
their concourse all that air which through the intervention of this shaded 
body cannot see the luminous body, and for this reason it becomes dark. 
As the body is equally enclosed the parts of the shadow become equal in 
respect to its centre, because all the parts of shaded bodies are also 
equidistant from their centre, and so every body has a centre in itself. 

As the above-named luminous lines are in contact with each extremity 
of the thing enclosed within them, they are equidistant from the middle 
of the length of any object that they enclose. 

That part of the primitive and derived shadow will be so much less 
dark as it is more distant from its centre. 

This comes about because the more the shadow separates from its 
centre the more it is seen by a greater quantity of luminous rays, and 
every man knows that where there is more light there is less shadow. 

c 17 r. 


If the sun is seen by all the seas which have the day, all these seas are 
seen by the sun. Therefore all the illumined water makes itself the 
mirror of the sun; and by its image all in the whole of this water and all 
in a part it appears to the eye. I ask therefore why when a ship is travel- 



ling and the sun sees itself, the eye does not see the sea all illumined, 
and why it does not always seem that the sun is travelling along the 
pathway of the boat. 


The sun makes as many pyramids as there are holes and crevices by 
which it can penetrate with its rays, and as many as the eyes of the 
animated beings that look upon it. Therefore as the sun finds itself 
always the base of each pyramid, the sun mirrored in the water seems 
to the eye to be as much beneath the water as it is outside it, and this sun 
thus reflected forms the base of the pyramid which ends in the eye. 
And this reflected sun will appear as great as the section of the pyramid 
cut by the surface of the water 2 X an \figure\ ^ ^ ^ 

Although the shaded and luminous body be of spherical rotundity 
and equal size, nevertheless its derived shadow will not resemble the 
rotundity of the body from which it proceeds, but will be of elongated 
shape if it falls within unequal angles. ^ ^ ^ ^ 

[Of the shapes of shadows'] 

The shapes of shadows often resemble the shaded body which is their 
origin, and often the luminous body which is their cause. 

If the shape and size of the luminous body are like that of the shaded 
body, the primitive and derived shadows will have the shape and size 
of these bodies, falling within equal angles. 

The derived shadow at a certain distance will never resemble the 
shape of the shaded body from which it proceeds, unless the shape of the 
light from this illuminating body resembles the shape of the body illumi- 
nated by the said light. 

Light that is long in shape will cause the derived shadow born from 
a round body to be wide and low, although it makes its percussion be- 
tween equal angles. 

It is impossible that the shape of the derived shadow should resemble 
that of the shaded body from which it was born, unless the light that 
causes it is similar in shape and size to this shaded body. c i8 v 

There will be as much difference in the darkness of two partially 
shaded rays as between the shadow that results from their blending and 
its first condition. 



It is impossible that from the blending of two complete shadows there 
should ensue a shadow darker in degree. 

It is possible that from the blending of two incomplete shadows may 
result a perfect shadow darker in degree than any of the former.^ c 19 r. 

Universally all the points that form the extreme points of the pyra- 
midal images of things are continually all in all the air, united and joined 
together without any intermission. 

Necessity causes that nature ordains or has ordained that in all points 
of the air all the images of the things opposite to them converge, by the 
pyramidal concourse of the rays that have emanated from these things; 
and if it were not so the eye would not discern in every point of the air 
that is between it and the thing seen, the shape and quality of the thing 
facing it. 

That pyramid which proceeds from its base with more unequal 
angles will be narrower, and will give a less accurate impression of the 
true width of the base. 

Among the many pyramids that are founded upon a single base that 
will be more powerful which is larger, and that will be larger which has 
the angles of its base more equal one to the other. 

The less the brightness of the derived as compared with that of the 
original light, the less will its pyramids illumine the spot on which they 

The pyramids will illumine the spot on which they strike the less 
as their angles are finer. caov. 

The farther the derived shadow extends from the primitive the 
brighter it becomes. 

Such proportion as the diameter of the derived shadow has to that 
of the primitive, you will find between the darkness of the primitive 
shadow and that of the derived. 

If the size of the illuminating body should surpass that of the body 
which is illumined, it will form an intersection of shadow, beyond which 
the divided shadows will pass off in two different directions, as though 
they derived from two different lights. 

That part of the derived shadow will be darker which is nearer to 
its source. 

^ Words crossed out in MS, 


. : . S 



Institut de France^ MS. C 19 r. 

[Text: II. 359-^3 i 







The above proposition holds good because, where the larger luminous 
angle is united to the narrower shaded angle, this luminous angle subdues 
it and almost changes it to its luminous nature. And so it is presumed 
that, where the larger shaded angle is united with the narrower luminous 
angle, the shaded will almost transform to its own nature the luminous 
that is joined to it. 

c 21 r. 

Of things which are the same in size and colour that which is farther 
away will seem lighter and less in bulk. 

The percussion of the derived shadow is always surrounded by 
shadow that melts into the luminous background. 

That part of the shaded body which is struck by the largest luminous 
angle will be more illuminated than any other. 

° ^ C 21 V. 

When there are several bodies of equal size which are equally distant I 

from the eye, that will appear the smaller which is against a more 
luminous background. 

Every visible body is surrounded by light and shade. 

Every perfectly round body when surrounded by light and shade ] 

will seem to have one of its sides greater than the other, in proportion 

as the one is more lighted than the other. 

° c 24 r. 

If the visual line that sees the shadow made by the light of the 

candle has an angle equal to that of the shadow, the shadow will almost 

seem to function beneath the body that causes it, as does the image of 

the bodies reflected by the water, for they are as much visible beneath it 

as above. Even so this shadow will so function that its extremity will 

appear to be as far below the surface on which it is produced, as the : [ 

summit of the body which causes it is above this surface, as is seen on 

a wall. ..v| 

c 25 r. '..'vi ^ i* 


The eye that finds itself between the light and shade which surround ; 

opaque bodies, will see there the shadow separated from the luminous . ■ 

part pass transversely through the centre of this body. 

When two objects are seen within the above-mentioned visual ' | 

pyramids, in such a way as not to fall short of or protrude beyond these 
lines, although there be a great intervening space between them, this 



distance, nevertheless, will never be capable of being seen or recognised 
by the eye. 

The greater the distance between the above-named bodies enclosed 
within visual pyramidal lines, the more necessary is it that there be a 
proportionate lack of conformity between them. c 27 r 


The first of the lights with which opaque bodies are illumined is 
called particular, and it is the sun or other light from a window or 
flame. The second is universal, as is seen in cloudy weather or in mist or 
the like. The third is the composite, that is when the sun in the evening 
or the morning is entirely below the horizon. ^ ^ ^ 

Among bodies in varying degrees of darkness deprived of the same 
light, there will be the same proportion between their shadows as there 
is between their natural degrees of darkness, and you have to understand 
the same of their lights. Ei 5r 


You will note in drawing how among shadows some are indistin- 
guishable in gradation and form; and this is proved by the fifth which 
says: — spherical surfaces have as many different degrees of light and 
shadow as there are varieties of brightness and darkness reflected from 
the objects round them. 

That part of an opaque body will be more in shadow or more in 
light which is nearer to the dark body which shades it, or to the luminous 
body which gives it light. 

The surface of every opaque body partakes of the colour of its 
object, but the impression is greater or less in proportion as this object 
is nearer or more remote, and of greater or less power. 

Objects seen between light and shadow will appear in greater relief 
than those which are in the light or in the shadow. e 17 r 

In the position of the eye which sees illuminated such part of plants 
as behold the light, one plant will never appear illuminated like 
the other. This is proved as follows:— let c be the eye that beholds the 
two plants ^ d which are illuminated by the sun a; I affirm that this eye c 


will not perceive the lights in the same proportion to their shadows in 
the one tree as in the other; for the tree that is nearer to the sun will 
show itself more in shadow than that farther away, in proportion as the 
one tree is nearer than the other to the concourse of the solar rays which 
come to the eye. i 

When a tree is seen from below, the eye sees the top of it set within i 

the circle formed by its branches. i 

Remember, O painter, that the degrees of depth of shade in one | 

particular species of tree vary as much as the sparseness or density of its 
ramifications. „ i 

E l8 V. 


As regards the equal diffusion of light, there will be the same pro- ; 

portion between the degrees of obscurity of the shadows produced, as [ 

there is between the degrees of obscurity of the colours to which these 
shadows are joined. 


The movement of the shadow is always more rapid than the move- 
ment of the body which produces it, if the luminous body be stationary. 

This may be proved: — let a be the luminous, b the shaded body, d the 
shadow. I say that the shaded body /A moves to c in the same time as the 
shadow d moves to and there is the same proportion of speed to speed 
over the same time as there is of length of movement to length of move- i 

ment. Therefore the proportion of the length of the movement made ^ 

by the shaded body b as far as c, to the length of the movement made by 
the shadow d as far as f , is such as the above-mentioned speeds of move- 
ment have to each other. I 

But if the luminous body be equal in speed to the movement of the 
shaded body, then the shadow and the shaded body will be of equal 
movements one to another. And if the luminous be swifter than the 
shaded body, then the movement of the shadow will be slower than the 
movement of the shaded body. i 

But if the luminous is slower than the shaded body then the shadow 
will be swifter than the shaded body. e^o v ^ 




The pyramidal shadow produced by the parallel body will be 
narrower than the shaded body, in proportion as the simple derived 
shadow is intersected at a greater distance from its shaded body. 


The simple derived shadows are of two kinds, that is to say one 
finite in length and two infinite. The finite is pyramidal, and of those 
that are infinite one is columnar and the other expanding. And all 
three have straight sides, but the convergent, that is the pyramidal 
shadow, proceeds from a shaded body that is less than the luminous 
body, the columnar proceeds from a shaded body equal to the 
luminous body, and the expanding from a shaded body greater than 
the luminous body. 


Compound derived shadows are of two kinds, that is, columnar and 


The difference that exists between light and lustre that reveals itself 
on the smooth surface of opaque bodies : — The lights that are produced 
on the smooth surfaces of opaque bodies will be stationary in stationary 
bodies, although the eye which sees them moves; but there will be lustres 
upon the same bodies in as many points of its surface as are the positions 
upon which the eye rests. 

Which bodies are those that have light without lustre? 

Opaque bodies which have a thick rough surface will never produce 
lustre in any portion of their illuminated part. 

Which bodies are those that have lustre and have no illuminated 

Thick, opaque bodies, with smooth surface, are those which have all 
the lustre in as many places, in the illuminated part, as there are positions 
that can receive the angle of the incidence of the light and of the eye, 
but, because such surface reflects all the things that surround the light, 
the illuminated body is not distinguishable in this part of the illuminated 

A luminous body of long shape will make the contours of its derived 
344 , 


shadow more indistinct than light that is spherical, and this it is that 
controverts the following proposition: — that shadow will have its contours 
more distinct which is nearer the primitive shadow, or if you prefer, the 
shaded body, but of this the long shape of the luminous body is the 


Derived shadows are of three kinds, of which one is expanding, 
another in the form of a column, the third converging at the point of 
the intersection of its sides which continue beyond in infinite length 
and straightness. And if you should say that this shadow is terminated 
in the angle formed by the meeting of its sides and does not pass beyond, 
this is controverted by the fact that, in the first concerning shadows, it 
was proved that a thing is entirely ended when no part of it exceeds its 
terminating lines; and, in the case of this shadow, one sees the contrary, 
inasmuch as where this derived shadow originates, there there are 
manifestly created the figures of two shaded pyramids which meet at 
their angles. If however as the adversary says, the first shaded pyramid 
terminates the derived shadow with its angle, from whence does the 
second shaded pyramid proceed? The adversary says that it is caused 
by the angle and not by the shaded body, but this is denied by the 
help of the second of this, which says: —the shadow is an accident created 
by the shaded bodies interposed between the position of this shadow 
and the luminous body. 

Thus it has become clear that the shadow is not produced by the 
angle of the derived shadow but only by the shaded body. 

If a spherical shaded body is illumined by an elongated luminous 
body, the shadow that is produced by the longest part of this luminous 
body will have its contours less defined than that produced by the 
breadth of the same light. And this is proved by what was said before, 
namely that that shadow is of less defined contours which is created by 
a greater luminous body, and conversely that shadow is of more defined 
contours 1 which is lit by a smaller luminous body. 

Broken shadows is the term given to those which are seen on a 
bright wall or other luminous object. 

That shadow will seem the darker which is against a lighter ground. 
^ di termini men noti. 


The contours of the derived shadows will be more distinct when 
they are nearer to the primitive shadow. 

The derived shadow will have the contours of its impress more 
distinct when they cut against the wall within more equal angles. 

That part of the same shadow will seem darker which has over 
against it darker objects; and that will seem less dark which is facing a 
brighter object. And the bright object when it is larger will shine more 

And that dark object which is of greater bulk will darken the derived 
shadow most in the place of its percussion. e 32 r 

The surface of every opaque bodyjshares in the colour of surrounding 

Shadow is the diminution of light. Darkness is the exclusion of light. 

Shadow is divided into two parts, of which the first is called primary 
shadow and the second derived shadow. 

Primary shadow always serves as a basis for derived shadow. 

The boundaries of derived shadows are straight lines. 

The darkness of the derived shadow diminishes in proportion as it is 
farther removed from primary shadow. 

That shadow will show itself darker which is surrounded by more 
dazzling brightness, and it will be less evident when it is produced on a 
darker ground. 

Particular light has as a result that it gives better relief to shaded 
bodies than does universal light; as may be shown by the comparison of 
the part of a landscape lit by the sun and that shaded by a cloud which 
is lit merely by the universal light of the air. ^ ^ ^ 



The surface of every opaque body partakes of the colour of its 
object. • 

That part of the surface of the opaque bodies partakes most of the 
colour of its object which is nearest to it. 

F I V. 

That part of a dark object of uniform thickness will show itself 
thinner which is seen against a more luminous background. 

That part of a luminous body of uniform thickness and radiance 
will seem thicker which is seen against a darker background. ^ ^ 





The ray of the sun after having passed through the bubbles of the 
surface of the water, sends to the bottom of the water an image of this 
bubble which bears the form of a cross. I have not yet investigated the 
cause, but I judge it to be a result of other small bubbles which are 
clustered together round the larger bubble. f 28 v 

A luminous hole seen from a dark place, though it be of uniform size, 
will seem to contract considerably when near to any object whatever 
that is interposed between the eye and this hole. 

This statement is proved by the seventh of this, which shows that 
the contours of any object interposed between the eye and the light will 
never be seen distinctly, but confused through the air becoming darker 
near these contours, this darkness becoming more intense the nearer it 
is to these contours. 

F 31 r. 

Two separated lights will at a certain distance appear joined and 

In this case it has been held by many who have made a study of 
perspective, that the air that surrounds these lights at a great distance is 
so illuminated that it seems of the nature of these lights, and therefore 
the light and air that surround them appear to be the same body. 

What they say is not true, for if it were the case that the air that 
surrounds these lights at a great distance was so illuminated as to appear 
all uniformly luminous, this would be more readily discerned near at 
hand where the exact shape of the light is known than it would be at a 
distance, and if, in becoming separated, the perception of the exact 
shape of this light is lost because it suffers a slight decrease in its radiance, 
how much more would be the diminution and loss of that radiance of 
the air, which is much less effulgent than the light! 

We shall prove therefore that this increase is caused by two images 
in the eye. 

The excessive brilliance of the light when near to the eye diminishes 
the visual faculty, seeing that the pupil being hurt contracts and so 
makes itself less, and as the light becomes more separated the injury to 
the eye ceases to exist, because the light has less brilliance, and so the 
pupil increases and sees a greater light. F^qv 



If there are two luminous bodies somewhat near to each other at a 
great distance they will seem united: 

This can happen for two reasons, of which the first is that in being 
near to these lights one knows instantly the distance or space that 
separates them, and the images of them that imprint themselves in our 
eye are still very distinct, and on the other hand their rays do not touch, 
whilst at a long distance these images look so near that not only their 
rays but the luminous bodies seem to touch. 

Further, at this distance the pupil which at first was contracted 
becomes enlarged, because the brilliance of the light is not as powerful 
as when it was near the eye, and so the eye increasing the size of its 
pupil sees a thing appearing enlarged. 

If all the images were to meet in an angle they would meet in a 
mathematical point, and this being indivisible all the different kinds 
would seem to you united; being united the sense would not be able to 
discern any difference. ^ t 

If some luminous body can be seen through a very small hole made 
in a piece of paper, approach the luminous body as nearly as possible 
with the eye; even though it still may be seen in its entirety it will seem 
so much less than before as this hole is of less size. . 

F 36 V. 

If the shape of the waves were in the figure of a half-circle, as are the 
bubbles of the water, the converging lines of the images of the sun, 
which emanate from these waves and come to the eye, would be of a 
very great angle, if this eye were upon the edge of the sea that comes 
between it and the sun. . 

Why does every luminous object that is of long shape appear round 
in the far distance? 

It is never a perfect round, but it happens with it as with the leaden 
die when beaten and much crushed that it appears round in shape. 
So this light at a great distance acquires such breadth in every direction, 
for as that which had been added is equal, and the first stock of light 
goes for nothing in comparison to what is added, the acquisition makes it 
appear uniformly round. 



And tliis serves to prove that the horns of every star are imperceptible 
at a great distance. ^ ^ 

O F L I G H T S 

The lights which illumine opaque bodies are of four kinds, that is to 
say, universal, as that of the atmosphere within our horizon, and particular, 
like that of the sun or of a window or door or other space; and the third 
is reflected light; and there is also a fourth which passes through 
substances of the degree of transparency of linen or paper or suchlike 
things, but not those transparent like glass or crystal or other diaphanous 
bodies, with which the effect is the same as if there was nothing interposed 
between the body in shadow and the light that illumines it; and of these 
we shall treat separately in our discourse. 

\Transparency of leave s\ 

The shadows in transparent leaves seen from the underside are the 
same shadows as those on the right side of this leaf, and the shadow is 
seen in transparency on the reverse at the same time as the luminous part; 
but the lustre can never show itself in transparency. ^ ^ ^ 

Of trees seen from below and against the light, one behind the other 
at a short distance, the topmost part of the first will be transparent and 
clear in great part, and it will stand out against the dark part of the 
second tree; and so it will be with all in succession which are situated 
under the same conditions. , 


The shadows of plants are never black, for where the atmosphere 
penetrates there cannot be utter darkness. . g 8 r 

[Foliage in lighi\ 

If the light comes from m and the eye is at n, this eye will see the 
colour of the leaves a b all affected by the colour of m, that is of the 
atmosphere, and that oib c will be seen on the underside in transparency, 
with a very beautiful green colour that verges on yellow. 

If m is the luminous body which lights up the leaf r, all the eyes that 
see the underside of the leaf will see it of a very beautiful light green 
because it is transparent. 

There will be many occasions when the positions of the leaves will be 


without shadows, and they will have the underside transparent and the 
right side shining. ^ g ^ 

The willow and other similar trees which are pollarded every third 
or fourth year put out very straight branches. Their shadow is towards 
the centre where these branches grow, and near their extremities they 
cast but little shade because of their small leaves and few and slender 

Therefore the branches which rise towards the sky will have but 
little shadow and little relief, and the branches which point downwards 
towards the horizon spring from the dark part of the shadow. And they 
become clearer by degrees down to their extremities, and show them- 
selves in strong relief being in varying stages of brightness against a 
background of shadow. 

That plant will have least shadow which has fewest branches and 
fewest leaves. 

G 9 r. 

The leaf of concave surface seen on the underside from below 
upward, will sometimes show itself half in shadow and half transparent. 
Thus let 0 pht the leaf, m the light and n the eye which will see o in 
shadow, because the light does not strike there between equal angles 
either on the right side or on the reverse; p is lit up on the right side, 
and its light is seen in transparency on its reverse. g lov 

o F S H A D o w S O N B O D I E S 

When you represent the dark shadows in shaded bodies, represent 
always the cause of the darkness, and you should do the same for 
reflections; this is because the dark shadows proceed from dark objects 
and the reflections from objects of but little brightness, that is from 
diminished lights. And there is the same proportion between the 
illuminated part of bodies and the part lit by reflection as there is between 

I the cause of the light on the bodies and the cause of the reflection. 

' G II "V. 

: That part of the tree will be seen to be clothed in shadows of least 

obscurity which is farthest away from the earth. 

IJ This may be proved: — let a pht the tree, nb c the illuminated hemi- 




sphere. The under part of the tree faces the earth / that is on the side 
0, and it faces a small part of the hemisphere at c d. But the highest 
part of the convexity a is visible to the greatest mass of the hemisphere, 
that is b c\ and for this reason, and because it does not face the darkness 
of the earth, it remains more illuminated. But if the tree is one thick 
with leaves, as the laurel, the arbutus, the box or the ilex, then it is 
different, for though a does not see the earth it sees the darkness of the 
leaves divided by many shadows, and this darkness is reflected upwards 
on to the undersides of the leaves above; and these trees have the 
shadows so much darker as they are nearer to the centre of the tree. 

G 12 r. 


When drawing any object, remember in comparing the potency of 
the lights of its illuminated portions, that the eye is often deceived into 
thinking one brighter than it really is. The reason springs from our 
comparing them with the parts which border on them, for if there are 
two parts of unequal degrees of brightness, and the less bright borders 
on a dark part while the brighter is set against a light background, such 
as the sky or some similar bright surface, then that which is less bright, 
or I should say less radiant, will appear more radiant and what was more 
radiant will seem darker. 

G 12 V. 


The painter deceives himself many times in representing the 
principal lights. ^ ^ 

Of representing an arrangement of bodies which receives the 
particular light of the sun or of another luminous body for its illumina- 


When the sun is in the east and the eye is above the centre of a 
city, the eye will see the southern part of this city with its roofs half 
in shadow and half in light, and the same towards the north; but those 
in the east will be entirely in shadow and those in the west entirely in 



The outlines and forms of each part of bodies in shadow are poorly- 
distinguished in their shadows and lights, but in such parts as are 
between the lights and shadows parts of these bodies are of the first 
degree of distinctness. 0321 


Take careful note of the situation of your figures, for you will have 
the light and shade different if the object is in a dark place with a 
particular light, and if it is in a bright place with the direct light of the 
sun, and different also if it is in a dark place with the diffused light of 
evening or in dull weather, and if it is in the diffused light of the 
atmosphere lit by the sun. 

^ ^ 33 

That part of the primary shadow will be least dark which is at the 
farthest distance from its extremities. 

The derived shadow which borders on the primary shadow will be 
darker than this primary shadow. H 66[i8] r 

That place will be most luminous which is farthest away from 
mountains. ^ ^ 

H 68 [ 20 ] r. 

The derived shadow is never like the body from which it proceeds, 
unless the light is of the shape and size of the body in shadow. 

The derived shadow cannot be like the primitive in shape unless it 
strikes within equal angles. h 76[28] v 



Because the luminous ray is of pyramidal power, and especially 
when the atmosphere is uniform, it will come about that when two rays 
emanating from equal lights meet in a straight line, the ray will be 
everywhere doubled and of uniform power; for where one has the apex 

of the pyramid the other has its base, 2ls n m shows. 

, ■ . . ■ •■■■•. I' 33 'r- ■ 

The imprint of the shadow of any body of uniform thickness will 
never resemble the body from whence it proceeds. 


Although a shaded body be pyramidal and equally distant in each 
of its parts from the luminous object, nevertheless that part of the 
pyramid which is smaller than the light that illumines it will not throw 
its shadow any distance from its cause. 

I 37 V. 

o F p A I N T I N G 

Shadows and lights are observed by the eye under three aspects. 
One of these is when the eye and the light are both on the same side of 
the body which is seen; the second is when the eye is in front of the 
object and the light behind it; and the third is that in which the eye is 
in front of the object and the light at the side, in such a way that when 
the line which extends from the object to the eye meets that which 
extends from the object to the light, they will at their junction ^ form a 
right angle. kioj CmIv. 

There is another division, namely that of the nature of the reflected 
object when placed between the eye and the light in different aspects. 

K io6 [z6] r. 


[Derived shadow] 

The derived shadow is stronger in proportion as it is nearer to its 

The same quality of shadow seems stronger in proportion as it is 
nearer to the eye. 

The percussion and section of the derived shadow is darker in pro- 
portion as it is shorter. k m r^il v. 

[Luminous rays] 

That part of the body will be illuminated which is struck by the 
luminous rays at more equal angles. m 77 v 

The image of the sun will show itself brighter in the small waves 
than in the large ones. This happens because the reflections or images 
of the sun occur more frequently in the small waves than in the large 
ones, and the more numerous brightnesses give a greater light than the 
lesser number. 

The waves which intersect after the manner of the scales of a fir-cone 
1 MS., cogutto^ and so Dr. Richter. M, Ravaisson-Mollien has cognition, 


reflect the image of the sun with the greatest splendour; and this occurs 
because there are as many images as there are ridges of the waves seen 
by the sun, and the shadows which intervene between these waves are 
small and not very dark; and the radiance of so many reflections is 
blended together in the image which proceeds from them to the eye, 
in such a way that these shadows are imperceptible. ^ ^ ^ 

There are two diflFerent kinds of light; the one is called free, the 
other restricted. The free is that which freely illuminates bodies; 
restricted is that which illuminates bodies in the same manner, through 
some hole or window. „ 

Lights are of two different natures, the one separated and the other 
united to bodies. 

Separated is that which illuminates the body, united is the part of 
the body illuminated by this light; the one light is called primary, the 
other derived. 

And so also there are shadows of two kinds; the one primary the 
other derived. Primary is that which is fastened to bodies, derived is 
that which is separated from bodies, bearing in itself to the surface of 
walls the resemblance of its cause. 

A simple shadow is one which does not see any light. 

A compound shadow is one which is illuminated by one or more 


A sieve through which penetrates the luminous air, at a great distance 
will seem without holes and entirely luminous. „ ' ' 

J Forster in 35 V. 

Between walls at an equal distance and quality which are seen 
behind the extremities of an opaque body set over against them, that part 
of the wall will appear more illuminated which is seen by a greater 
amount of the pupil. ^ 

r r Forster III 36 r. 

Among things of equal distance and size that which has the greater 
light wiU seem of greater body. ^ 

If the illuminated object is the size of the thing that illuminates, 

m ■ 


and of that where this light is reflected, the quality of the reflex light 
will have the same proportion to the intermediate light as this second 
liffht has to the first, if these bodies are smooth and white. „ 

O ’ Forster III 54 r. 

The luminous or illuminated object contiguous to the shadow cuts 
as much as it touches. 

There will be as much lacking in the extremities of the shadows of 
bodies as is touched by the illuminated or luminous field. „ „ 

\Of shadow\ 

Shadow is the diminution of light and of darkness, and it is inter- 
posed between darkness and light. 

Shadow is of infinite obscurity, and this obscurity may be infinitely 

The beginnings and the ends of shadow extend between light and 
darkness, and they may be infinitely diminished and increased. 

Shadow is the expression of bodies and of their shapes. 

The shapes of bodies will convey no perception of their quality 
without shadow. 

Shadow partakes always of the colour of its object. 

Of the boundaries of shadows: some are like smoke, with boundaries 
that cannot be perceived, in others they are distinct. 

Keep the drawings for the end of the [book on] shadows. They may 
be seen in the workshop of Gherardo the miniaturist in San Marco at 

No opaque body is without shadow or light, except when there is a 
mist lying over the ground when it is covered with snow, or it is the 
same when it snows in the country; this will be without light and it will 
be surrounded by darkness. 

And this occurs in spherical bodies, because in the case of other 
bodies which have members, the parts of the members which face each 
other steep each other in the tone of their surface. 

The surface of every body is infused into all the illuminated air 
which serves as its object. 

The surface of opaque bodies has its whole image in all the illu- 
minated air which surrounds it from every quarter. 

Make the rainbow in the last book ‘On Painting’. But first make the 
book of the colours produced by the mixture of the other colours^ so 



that by means of these colours used by painters you may be able to prove 
the genesis of the colours of the rainbow. 

Describe how no body is in itself defined in the mirror; but the eye 
on seeing it in this mirror puts boundaries to it; for if you cause your face 
to be represented in the mirror the part is like the whole, seeing that the 
part is all in the whole of the mirror and it is complete in every part of 
the same mirror; and the same happens with every image of every object 
set in front of this mirror. 

The boundaries of the derived shadow are surrounded by the colours 
of the illuminated objects which are round the luminous body, the cause 
of this shadow. 

Derived shadow does not exist without primary light: this is proved 
by the First of this, which states that darkness is the entire privation of 
light, and shadow is the gradual diminution of darkness and of light; 
and it partakes so much the more or the less of darkness than of light 
in proportion as the darkness has been broken up by this light. 

What is the cause which makes the boundaries of the shadow con- 
fused and indistinct. 

Whether it is possible to give the contours of the shadows clear-cut 

and precise boundaries. j • /: 

r ^uaderni nor. 

[0/ luminous bodie5\ 


Of bodies equal in size and distance that which is most luminous 
tinges most with its essence the opposite object. 

Of bodies of equal luminosity that which is largest in outline tinges 
most of the surface of its object, the distance of all being equal. 

Of bodies which are equal in luminosity and size that which is 
nearest tinges its object most. ^ i ^ 

° Quaderm ii i6 r. 

The reason why we know that light has in itself a single centre is as 
follows:— we recognise clearly that a large light often outspans a small 
object, which nevertheless, although it surrounds it much more than 
twice with its rays, always has its shadow appearing on the first surface 
and it is always visible. 

Let c/be the large light and n the object in front of it which pro- 
duces the shadow on the wall, and a b the wall; it clearly appears that 
jt is not the large light that will cast the shadow of n upon the wall; but 




since the light has a centre in itself I prove by experiment the shadow is 
cast upon the wall as is shown 2.tmotr, \piagram\ 

Why to two or in front of two eyes do three things when represented 
appear as two. 

Why in surveying a direction with two sights the first appears untrue. 

I say the eye projects an infinite number of lines, and these attach 
themselves to or mingle with those that come towards it which emanate 
from the things seen, and only the centre line of this perceptive faculty 
is that which knows and judges bodies and colours; all the others are 
false and deceitful. 

And when you place two things at a distance of a cubit one from the 
other, the nearer being close to the eye, the surface of this nearer one 
will remain far more confused than that of the second, the reason being 
that the nearer is overrun by a greater number of false lines than the 
second and so is more uncertain. 


Light acts like this because in the effects of its lines and especially 
in the working of its perspective it is very similar to the eye; and its 
centre ray carries truth in its testing of shadows. When the object placed 
in front of it is too rapidly subdued by dim rays, it will cast a shadow 
broad and disproportionately large and ill defined; but when the object 
that has to produce the shadow cuts the rays of the light and is near the 
place of percussion, then the shadow becomes distinct; and this especially 
when the light is at a distance, because the centre ray at a long distance 
is less interfered with by false rays, seeing that the lines of the eye and 
the solar and other luminous rays proceeding through the air are obliged 
to keep a straight course. Otherwise if they were impeded by the 
atmosphere being denser or more rarefied they would remain bent at 
some point, but if the air is free from heaviness or humidity they will 
observe their straight nature, always carrying back to their point of 
origin the image of the intercepting object, and if it is the eye the 
intercepting object will be estimated by its colour as well as by its shape 
and size. But if the surface of the said interposing object shall have 
within it some small hole that enters into a room dark not on account of 
its colour but through absence of light, you will see the rays entering 
through this small hole transmitting there, to the wall beyond, all the 
traits of their original both as to colour and form, except that everything 
will be inverted. Windsor: Drawings 19148 V. 



The way in which the images of bodies intersect at the edges of 
the small holes by which they penetrate: 

What difference is there between the manner of penetration of the 
images which pass through narrow apertures and those which pass 
through wide ones or those which pass at the sides of shaded bodies. 


The images ofthe immovable objects move by the moving of the edges 
of that aperture through which the rays of the images penetrate, and 
this comes about by the ninth [section] which says:— the images of any 
body are all in all and all in every part of the area that is round about 
them. It follows that the moving of one of the edges of the aperture by 
which these images penetrate to a dark place releases the rays of the 
images that were in contact with it, and they unite with other rays of 
those images which were remote from it. 

U P P E R O R L O W E R E D G E 

If you move the right side of the opening the impression on the left 
will move, being that of the object on the right which entered by this 
opening, and the same will happen with all the other sides of this 
opening, and this is proved with the help of the second [section] of this 
[treatise] which says: — all the rays which carry the images of bodies 
through the air are straight lines. Therefore as the images of the greatest 
bodies have to pass through the smallest openings, and beyond this 
opening to re-form in their utmost expansion, it is necessary that this 
intersection be uninterrupted. • 

r Windsor: Drawings 19 149 r. 

The images of bodies are all diffused through the air which sees 
them and all in every part of it. 

This is proved: — ht a c and e be objects, of which the images 
penetrate to a dark place by the small holes ;z />, and imprint themselves 
on the wall/ 1? opposite to these holes; as many impressions will be made 
at as many different places on this wall as is the number of the said small 

Royal Library^ Windsor 



All the smallest parts of the images penetrate one another without 
occupation the one of the other. ... 

. . . the seventh of this where it is said:— every simulacrum sends forth 
from itself its images by the shortest line, which of necessity is straight. 

Windsor: Drawings 191 50 V. 

Demonstration how every part of light converges in a point. 

Although the balls a B c have their light from one window, never- 
theless if you follow the lines of their shadows you will see that they 
make intersection and point in the angle n. , 

^ ° Windsor MSS. R 137 

Shadow is light diminished by means of the intervention of an opaque 
body. Shadow is the counterpart of the luminous ray cut off by an 
opaque body. 

This is proved because the shaded ray is of the same shape and size 
as was the luminous ray in which this shadow projects itself. 

Windsor: Drawings 1 9 1 5 2 V. 

Demonstration and argument why of parts in light some portions 
are in higher light than others. 


Since it is proved that every light with fixed boundaries emanates 
or appears to emanate from a single point, that part illuminated by it 
will have those portions in highest light upon which the line of radiance 
falls, between two equal angles, as is shown above in the lines a g^ also 
in a and similarly in and that portion of the illuminated part will 
be less luminous upon which the line of incidence strikes at two more 
unequal angles, as may be seen in h r and and in this way you will also 
be able to discern the parts deprived of light, as may be seen at m and h 

When the angles made by the lines of incidence are more equal the 
place will have more light, and where they are more unequal it will be 

I will treat further of the cause of the reflection. , 




‘Perspective is a rational demonstration whereby 
experience confirms how all things transmit their 
images to the eye by pyramidal lines.’ 

Sandro! you do not say why these second things seem lower than 
the third. ^ 


The eye between two parallel lines will never see them at so great a 
distance that they meet in a point. 

•> ^ C.A. i2or. d 

All the cases of perspective are expressed by means of the five 
mathematical terms, to wit: point, line, angle, surface and body. Of 
these the point is unique of its kind, and this point has neither height 
nor breadth, nor length nor depth, wherefore we conclude that it is 
indivisible and does not occupy space. A line is of three kinds, namely 
straight, curved and bent, and it has neither breadth, height nor depth, 
consequently it is indivisible except in its length; its ends are two points. 

An angle is the ending of two lines in a point, and they are of three 
kinds, namely right angles, acute angles and obtuse angles. 

Surface is the name given to that which is the boundary of bodies, 
and it is without depth, and in such depth as it has it is indivisible as is 
the line or point, being divided only in respect of length or breadth. 
There are as many different kinds of surfaces as there are bodies that 
create them. 

Body is that which has height, breadth, length and depth, and in 
all these attributes it is divisible. These bodies are of infinite and varied 
forms. The visible bodies are of two kinds only, of which the first is 
without shape or any distinct or definite extremities, and these though 
present are imperceptible and consequently their colour is difficult to 
determine. The second kind of visible bodies is that of which the 
surface defines and distinguishes the shape. 

The first kind, which is without surface, is that of those bodies which 
are thin or rather liquid, and which readily melt into and mingle with 
other thin bodies, as mud with water, mist or smoke with air, or the 
element of air with fire, and other similar things, the extremities of which 
are mingled with the bodies near to them, whence by this intermingling 
their boundaries become confused and imperceptible, for which reason 

^ Fragment probably of a discussion with Botticelli concerning the law of diminishing 
perspective. References to Sandro [Botticelli] are also to be found in c.a. 3^3 I’j P* 555) 
and (Ludwig) 6o, 



they find themselves without surface, because they enter into each other’s 
bodies, and consequently such bodies are said to be without surface. 

The second kind is divided into two other kinds, namely transparent 
and opaque. The transparent is that which shows its whole self along 
the whole of its side, and nothing is hidden behind it, as is the case with 
glass, crystal, water and the like. The second division of bodies of which 
the surface reveals and defines the shape is called opaque. 

This it behoves us to treat of at some length, seeing that out of it are 
derived an infinite number of cases. , 


The air is full of an infinite number of images of the things which 
are distributed through it, and all of these are represented in all, all in 
one, and all in each. Consequently it so happens that if two mirrors be 
placed so as to be exactly facing each other, the first will be reflected 
in the second and the second in the first. Now the first being reflected 
in the second carries to it its own image together with all the images 
which are represented in it, among these being the image of the second 
mirror; and so they continue from image to image on to infinity, in 
such a way that each mirror has an infinite number of mirrors within it, 

each smaller than the last, and one inside another. 

By this example, therefore, it is clearly proved that each thing 
transmits the image of [itself] to all those places where the thing itself is 
visible, and so conversely this object is able to receive into itself all the 
images of the things which are in front of it. 

Consequently the eye transmits its own image through the air to all 
the objects which are in front of it, and receives them into itself, that is 
on its surface, whence the understanding takes them and considers 
them, and such as it finds pleasing, these it commits to the memory. 

So I hold that the invisible powers of the images in the eyes may 
project themselves forth to the object as do the images of the object to 
the eye. 

An instance of how the images of all things are spread through the 
air may be seen in a number of mirrors placed in a circle, and they will 
then reflect each other for an infinite number of times, for as the image of 
one reaches another it rebounds back to its source, and then becoming 
less rebounds yet again to the object, and then returns, and so continues 
for an infinite number of times. 



If at night you place a light between two flat mirrors which are 
a cubit’s space apart, you will see in each of these mirrors an infinite 
number of lights, one smaller than another, in succession. 

If at night you place a light between the walls of a [room], every 
part of these walls will become tinged by the images of this light, and 
all those parts which are exposed to the light will likewise be directly 
lit by it; that is when there is no obstacle between them to interrupt the 
transmission of the images. 

This same example is even more apparent in the transmission of 
solar rays, which all [pass] through all objects, and consequently into 
each minutest part of each object, and each ray of itself conveys to its 
object the image of its source. 

That each body alone of itself fills the whole surrounding air with 
its images, and that this same air is [able] at the same time to receive into 
itself the images of the countless other bodies which are within it, is 
clearly shown by these instances; and each body is seen in its entirety 
throughout the whole of the said atmosphere, and each in each minutest 
part of the s'kme, and all throughout the whole of it and all in each 
minutest part; each in all, and all in every part, c a 138 r b 

O F P A I N T I N G 

The true knowledge of the form of an object becomes gradually 
lost in proportion as distance decreases its size. ca 176 V b 

\With drawingl 

Body formed from the perspective by Leonardo Vinci, disciple of 

This body may be made without the example of any other body but 
merely with plain lines. 

-T C.A. 191 r. a 

Among the various studies of natural processes, that of light gives 
most pleasure to those who contemplate it; and among the noteworthy 
characteristics of mathematical science, the certainty of its demonstrations 
is what operates most powerfully to elevate the minds of its investigators. 

Perspective therefore is to be preferred to all the formularies and 
systems of the schoolmen, for in its province the complex beam of light 
is made to show the stages of its development, wherein is found the glory 
not only of mathematical but also of physical science, adorned as it is 


with the flowers of both. And whereas its propositions have been 
expanded with much circumlocution I will epitomise them with con- 
clusive brevity, introducing however illustrations drawn either from 
nature or from mathematical science according to the nature of the 
subject, and sometimes deducing the results from the causes and at other 
times the causes from the results; adding also to my conclusions some 
which are not contained in these, but which nevertheless are to be 
inferred from them; even as the Lord who is the Light of all things shall 
vouchsafe to reveal to me, who seek to interpret this light — and conse- 
quently I will divide the present work into three parts. 

Light, when in the course of its incidence it sees things which have 
been turned against itself, retains their images in part. This conclusion 
is proved by results, because the vision as it looks upon the light has a 
measure of fear. Even so after the glance there remain in the eye the 
images of vivid objects, and they make the place of lesser light appear in 
shadow until the eye has lost the trace of the impression of the greater 

° C.A. 203 r. a 

M E T H O D S O F P E R S P E C T I V E 

If you wish to represent a figure in the corner of a dwelling which 
shall appear to have been made in a level place, get someone to strip 
naked, and with the light of a candle make their shadow fall as you wish 
in the said corner, and draw the outline of it with charcoal; but your sight 
will wish to be in the spot exactly through a hole placed where the light 
passed, and again the light of the window after its work will wish to 
come by the said line, so that the walls joined together in the corner 
will not be any darker on account of the shadow, the one than the other. 


That the light has not any difference from the eye as regards losing 
the thing which is behind the first object is due to this reason: you know 
that in swiftness of movement and in concourse of straight lines the 
visual ray and the ray of light resemble each other. As an example: 
suppose you hold a coin near to the eye, that space which exists between 
the coin and the boundary of the position, will be more capable of 
expansion^ in proportion as the part of the boundary of the position 



; which is not visible to the eye is the greater, and the nearer the coin 

is brought to the eye the more the boundary of the position will be 
filled up. 


Of the eye. The same process may be seen with light, for as you 
bring the said coin nearer or remove it farther from this light you will 
see the shadow on the opposite wall growing larger or failing, and if 

I you wish an example let it be in this form: have many bodies of different 

things placed in a large room, then take in your hand a long pole with 

I a piece of charcoal at the point and mark with that on the ground and 

I along the walls all the outlines of the things^ as they appear against the 

i boundaries of the wall. 

Of the light. Then at the same distance and height place a light, 
and you will see the shadows of the said bodies covering as much of the 
wall as the part that found itself enclosed within the marks made by the 
charcoal placed at the point of the pole. 


If you wish to see a similar experiment place a light upon a table, and 
then retire a certain distance away, and you will see that all the shadows 
of the objects which are between the wall and the light remain stamped 
with the shadow of the form of the objects, and all the lines of their 
length converge in the point where the light is. 

Afterwards bring your eye nearer to this light, using the blade of a 
knife for a screen so that the light may not hurt your eye, and you will 
see all the bodies opposite without their shadows, and the shadows 
which were in the partitions of the walls will be covered as regards the 

ii eye by the bodies which are set before them. , , 

i I J J C.A. 204 V. b 

Of things of equal size situated at an equal distance from the eye, 
that will appear the larger which is whiter in colour. 

Equal things equally distant from the eye will be judged by the 
eye to be of equal size. 

Equal things through being at different distances from the eye 
come to appear of unequal size. 

1 Reading M’^.'ha&delle pariete^ 

I ^^7 

I " 


Unequal things by reason of their different distances from the eye 
may appear equal. cA.aaiv.c 

Many things of great bulk lose their visibility in the far distance by 
reason of their colour, and many small things in the far distance retain 
their visibility by reason of the said colour. 

An object of a colour similar to that of the air retains its visibility 
at a moderate distance, and an object that is paler than the air retains it 
in the far distance, and an object which is darker than the air ceases to 
be visible at a short distance. 

But of these three kinds of objects that will be visible at the greatest 
distance of which the colour presents the strongest contrast to itself. 

C.A, 249 r. c 


That dimness (il mezzo confuso) which occurs by reason of distance, 
or at night, or when mist comes between the eye and the object, causes 
the boundaries of this object to become almost indistinguishable from 
the atmosphere. c.A.,i6y.b 

An object placed between the eye and an object of dazzling white- 
ness loses half its size. , 

C.A. 320 V. b 


If you place a candle between two tall mirrors shaped like curved 
roofing tiles in the manner here sh.own \drawing\y you will see every- 
thing that offers resistance melted in this candle with the help of these 

cjv. 338 r. a 

If you wish to furnish a proof of how things seen by the eye diminish, 
it is necessary to fix the eye on the centre of the wall, and the curve of the 
wall will then give you the true clearness of the things seen. 

When the cause of the shadow is near the place where it strikes and 
distant from the light, you will see the shape of the cause of the severed 
rays clearly upon the wall. , 

Among things of equal size, that will show itself less inform which is 

farther away from the eye. 

• 353 v.b 


P E R S P E C T I V E 

It IS asked of you, O painter, why the figures which you draw on a 
minute scale as a demonstration of perspective do not appear — not- 
withstanding the demonstration of distance -- as large as real ones, 
which are of the same height as those painted upon the wall. 

And why [representations of] things, seen a short distance away, 
notwithstanding the distance, seem larger than the reality. Tr 66 a 


Perspective is nothing else than the seeing of an object behind a sheet 
of glass, smooth and quite transparent, on the surface of which all the 
things may be marked that are behind this glass; these things approach 
the point of the eye in pyramids, and these pyramids are cut by the said 

° ■ A I V. 

Citation, of the things that I ask to have admitted in the proofs of this 
my perspective: — I ask that it may be permitted me to affirm that every 
ray which passes through air of uniform density proceeds in a direct line 
from its cause to its object or the place at which it strikes. 


A second object as far removed from the first as the first is from the 
eye will appear half the size of the first, although they are of the same 

A small object near at hand and a large one at a distance, when seen 
between equal angles will appear the same size. 

I ask how far away the eye can see a non-luminous body, as for 
instance a mountain. It will see it to advantage if the sun is behind it, and 
it will seem at a greater or less distance away according to the sun’s place 
in the sky. 

Perspective is a rational demonstration whereby experience confirms 
how all things transmit their images to the eye by pyramidal lines. By 
pyramidal lines I mean those which start from the extremities of the sur- 
face of bodies, and by gradually converging from a distance arrive at the 


same point; the said point being, as I shall show, in this particular case 
located in the eye, which is the universal judge of all objects. I call a point 
that which cannot be divided up into any parts; and as this point which 
is situated in the eye is indivisible, no body can be seen by the eye which 
is not greater than this point, and this being the case it is necessary that 
the lines which extend from the object to the point should be pyramidal. 
And if anyone should wish to prove that the faculty of sight does not 
belong to this point, but rather to that black spot which is seen in the 
centre of the pupil, one might reply to him that a small object never 
could diminish at any distance, as for example a grain of millet or panic- 
seed or other similar thing, and that this thing which was greater than 
the said point could never be entirely seen. ^ ^ 

No object can be of so great a size as not to appear less to the eye at a 
great distance than a smaller object which is nearer. 

A wall surface is a perpendicular plane represented in front of the 
common point at which the concourse of the pyramids converges. And 
this wall surface performs the same function for the said point as a flat 
piece of glass upon which you drew the various objects that you saw 
through it, and the things drawn would be so much less than the originals, 
as the space that existed between the glass and the eye was less than that 
between the glass and the object. 

The concourse of the pyramids created by the bodies will show upon 
the wall surface the variety of the size and distance of their causes. 

All these planes which have their extremities joined by perpendicular 
lines forming right angles must necessarily, if of equal size, be less visible 
the nearer they rise to the level of the eye, and the farther they pass 
beyond it the more will their real size be seen. 

The farther distant from the eye is the spherical body, the more it is 

A 10 V. 

As soon as ever the air is illuminated it is filled with an infinite num- 
ber of images, caused by the various substances and colours collected 
together within it, and of these images the eye is the target and the 



All things transmit their image to the eye by means of pyramids; 

370 ■ 


the nearer to the eye these are intersected the smaller the image of their 
cause will appear. ■ 


If you should ask how you can demonstrate these points to me from 
experience, I should tell you, as regards the vanishing point which moves 
with you, to notice as you go along by lands ploughed in straight furrows, 
the ends of which start from the path where you are walking, you will 
see that continually each pair of furrows seem to approach each other and 
to join at their ends. 

As regards the point that comes to the eye, it may be comprehended 
with greater ease; for if you look in the eye of anyone you will see your 
own image there; consequently if you suppose two lines to start from 
your ears and proceed to the ears of the image which you see of yourself 
in the eye of the other person, you will clearly recognise that these lines 
contract so much that when they have continued only a little way be- 
yond your image as mirrored in the said eye they will touch one another 
in a point. 

A 37 r. and V. 

The thing that is nearer to the eye always appears larger than 
another of the same size which is more remote. 

A 38 r. 

Perspective is of such a nature that it makes what is flat appear in 
relief, and what is in relief appear flat. a 38 V 

The perspective by means of which a thing is represented will be 
better understood when it is seen from the view-point at which it was 

If you wish to represent a thing near, which should produce the effect 
of natural things, it is impossible for your perspective not to appear false, 
by reason of all the illusory appearances and errors in proportion of 
which the existence may be assumed in a mediocre work, unless whoever 
is looking at this perspective finds himself surveying it from the exact 
distance, elevation, angle of vision or point at which you were situated to 
make this perspective. Therefore it would be necessary to make a win- 
dow of the size of your face or in truth a hole through which you would 
look at the said work. And if you should do this, then without any doubt 
your work will produce the eflPect of nature if the light and shade are 
correctly rendered, and you will hardly be able to convince yourself that 
. . ■■■ 371 ' ■ ■ . 


these things are painted. Otherwise do not trouble yourself about repre- 
senting anything, unless you take your view-point at a distance of at 
least twenty times the maximum width and height of the thing that you 
represent; and this will satisfy every beholder who places himself in front 
of the work at any angle whatever. 

If you wish to see a proof of this quickly, take a piece of a staff like a 
small column eight times as high as its width without plinth or capital, 
then measure off on a flat wall forty equal spaces which are in conformity 
with the spaces; they will make between them forty columns similar 
to your small column. Then let there be set up in front of the middle 
of these spaces, at a distance of four braccia from the wall, a thin band of 
iron, in the centre of which there is a small round hole of the size of a 
large pearl; place a light beside this hole so as to touch it, then go and 
place your column above each mark of the wall and draw the outline of 
the shadow, then shade it and observe it through the hole in the iron. 

, A 40 V. 

In Vitolone there are eight hundred and five conclusions about 
perspective. BsSr. 


No visible body can be comprehended and well judged by human 
eyes, except by the difference of the background where the extremities 
of this body terminate and are bounded, and so far as its contour lines 
are concerned no object will seem to be separated from this background. 
The moon, although far distant from the body of the sun, when by reason 
of eclipses it finds itself between our eyes and the sun, having the sun 
for its background will seem to human eyes to be joined and attached 

Perspective comes to aid us where judgment fails in things that 

C 27 V. 

\Of perspective in nature and in art\ 

It is possible to bring about that the eye does not see distant objects 
as much diminished as they are in natural perspective, where they are 
diminished by reason of the convexity of the eye, which is obliged to 
intersect upon its surface the pyramids of every kind of image that 
approach the eye at a right angle. But th^ method that I show here in 

^ ' r ' - 


the margin cuts these pyramids at right angles near the surface of the 
pupil. But whereas the convex pupil of the eye can take in the whole ot 
our hemisphere, this will show only a single star; but where many smal 
stars transmit their images to the surface of the pupil these stars are very 
small; here only one will be visible but it will be large; and so the moon 
will be greater in size and its spots more distinct. You should place close 
to the eye a glass filled with the water mentioned in [chapter] four of 
book 1 13 ‘Concerning Natural Things’, water which causes things 
congealed in balls of crystalline glass to appear as though they were 

without glass. ^ 1 • 

Of the eye. Of bodies less than the pupil of the eye that which is 
nearest to it will be least discerned by this pupil — ■ and from this 
experience it follows that the power of sight is not reduced to a 

^ But the images of objects which meet in the pupil of the eye are 
spread over this pupil in the same way as they are spread about in the 
air; and the proof of this is pointed out to us when we look at the starry 
heavens without fixing our gaze more upon one star than upon another, 
for then the sky shows itself to us strewn with stars, and they bear to the 
eye the same proportions as in the sky, and the spaces between them also 
are the same. e 15 v. 

Natural perspective acts in the opposite way, for the greater the 
distance the smaller does the thing seen appear, and the less the distance 
the larger it appears. But this invention constrains the beholder to stand 
with his eye at a small hole, and then with this small hole it will be seen 
well. But since many eyes come together to see at the same tinie one 
and the same work produced by this art, only one of them will have a 
good view of the function of this perspective and all the others will only 
see it confusedly. It is well therefore to shun this compound perspective, 
and to keep to the simple which does not purport to view planes tore- 
shortened but as far as possible in exact form. ^ 

And of this simple perspective in which the plane intersects the 
pyramid that conveys the images to the eye that are at an equal distance 
from the visual faculty, an example is afforded us by the curve of the 
pupil of the eye upon which these pyramids intersect at an equal distance 
from the visual faculty. E i6r. 



A P P E A R S L E S S 

The practice of perspective is divided into [two] parts, of which the 
first treats of all the things seen by the eye at whatsoever distance, and 
this in itself shows all these things diminished as the eye beholds them, 
without the man being obliged to stand in one place rather than in 
another, provided that the wall does not foreshorten it a second time. 

But the second practice is a combination of perspective made partly 
by art and partly by nature, and the work done according to its rules has 
no part that is not influenced by natural and accidental perspective. 
Natural perspective I understand has to do with the flat surface on which 
this perspective is represented; which surface, although it is parallel to 
it in length and height, is constrained to diminish the distant parts more 
than its near ones. And this is proved by the first of what has been said 
above, and its diminution is natural. 

Accidental perspective, that is that which is created by art, acts in 
the contrary way; because it causes bodies equal in themselves to increase 
on the foreshortened plane, in proportion as the eye is more natural and 
nearer to the plane, and as the part of this plane where it is represented 
is more remote from the eye. . 

J E 10 V. 

If the true outlines of opaque bodies become indistinguishable at any 
short distance they will be still more invisible at great distances; and 
since it is by the outlines that the true shape of each opaque body be- 
comes known, whenever because of distance we lack the perception of 
the whole we shall lack yet more the perception of its parts and outlines. 

E 8o r. 


There are three divisions of perspective as employed in painting. 
Of these the first relates to the diminution in the volume of opaque 
bodies; the second treats of the diminution and disappearance of the 
outlines of these opaque bodies; the third is their diminution and loss of 
colour when at a great distance. 




Among opaque bodies of equal magnitude, the diminution apparent 
in their size will vary according to their distance from the eye which 
sees them; but it will be in inverse proportion, for at the greater distance 
the opaque body appears less, and at a less distance this body will appear 
greater, and on this is founded linear perspective. And show secondly 
how every object at a great distance loses first that portion of itself which 
is the thinnest. Thus with a horse, it would lose the legs sooner than the 
head because the legs are thinner than the head, and it would lose the 
neck before the trunk for the same reason. It follows therefore that 
the part of the horse which the eye will be able last to discern will be 
the trunk, retaining still its oval form, but rather approximating to the 
shape of a cylinder, and it will lose its thickness sooner than its length 
from the second conclusion aforesaid. If the eye is immovable the per- 
spective terminates its distance in a point; but if the eye moves in a 
straight line the perspective ends in a line, because it is proved that the 
line is produced by the movement of the point, and our sight is fixed 
upon the point, and consequently it follows that as the sight moves the 
point moves, and as the point moves the line is produced. ^ ^ 

Of objects of equal size placed at equal distances from the eye the 
more luminous will appear the greater. 

Of equal objects equally distant from the eye the more obscure will 
appear the less. - 

Of things removed an equal distance from the eye that will appear to 
be less diminished which was at first more. 

Of things removed from the eye at an equal distance from their first 
position, that is less diminished wHch at first was more distant from this 

And the proportion of the diminution will be the same as that of the 
distances at which they were from the eye before their movement. 


Simple perspective is that which is made by art upon a position 
equally distant from the eye in each of its parts. 


Complex perspective is that which is made upon a position in which 
no two of the parts are equally distant from the eye. G13V 


If two similar and equal things be placed one behind the other at a 
given distance, the difference in their size will appear greater in propor- 
tion as they are nearer to the eye which sees them. And conversely there 
will appear less difference in size between them as they are farther 
removed from the eye. 

This is proved by means of the proportions that they have between 
their distances, for if there are two bodies with as great a distance from 
the eye to the first as from the first to the second this proportion is called 
double; because if the first is one braccio distant from the eye and the 
second is at a distance of two braccia, the second space is double the first, 
and for this reason the first body will show itself double the second. 
And if you remove the first to a distance of a hundred braccia and the 
second to a hundred and one braccia, you will find that the first is greater 
than the second by the extent to which a hundred is less than a hundred 
and one, and this conversely. 

The same thing also is proved by the fourth of this, which says: in 
the case of equal things there is the same proportion of size to size as that 
of distance to distance from the eye that sees them. 

•' G 29 V. 


Perspective as it concerns Painting is divided into three chief parts, 
of which the first treats of the diminution in the size of bodies at different 
distances. The second is that which treats of the diminution in the colour 
of these bodies. The third of the gradual loss of distinctness of the forms 
and outlines of these bodies at various distances. 

Perspective employs in distances two opposite pyramids, one of which 
has its apex in the eye and its base as far away as the horizon. The other 
has the base towards the eye and the apex on the horizon. But the first 
is concerned with the universe, embracing all the mass of the objects that 
pass before the eye, as though a vast landscape was seen through a small 
hole, the number of the objects seen through such a hole being so much 
the greater in proportion as the objects are more remote from the eye; 
and thus the base is formed on the horizon and the apex in the eye, as I 
have said above. 



The second pyramid has to do with a peculiarity of landscape, in 
showing itself so much smaller in proportion as it recedes farther from 
the eye; and this second instance of perspective springs from the first. 

\Ferspectwe of disappearance^ 

In every figure placed at a great distance you lose first the know- 
ledge of its most minute parts, and preserve to the last that of the larger 
parts, losing, however, the perception of all their extremities; and they 
become oval or spherical in shape, and their boundaries are indistinct. 


The eye cannot comprehend a luminous angle when close to itself. 

h7i [23] r. 


The shadows or reflections of things seen in moving water, that is to 
say with tiny waves, will always be greater than the object outside the 
water which causes them. 

The eye cannot judge where an object high up ought to descend. 

H 76 [28] V. 

No surface will reveal itself exactly if the eye which sees it is not 
equally distant from its extremities. H 8 i [33]r 

O F O R D I N A R Y P E R S P E C T I V E 

An object of uniform thickness and colour seen against a background 
of various colours will appear not to be of uniform thickness. 

And if an object of uniform thickness and of various colours is seen 
against a background of uniform colour, the object will seem of a varying 

And in proportion as the colours of the background, or of the object 
seen against the background, have more variety, the more will their 
thickness seem to vary, although the objects seen against the background 
may be of equal thickness. ^ i i7v 

A dark object seen against a light background will seem smaller 
than it is. 

A light object will appear greater in size when it is seen against a 
background that is darker in colour. ^ ^ 



If the eye be in the middle of a course with two horses running to 
their goal along parallel tracks, it will seem to it that they are running to 
meet one another. 

This that has been stated occurs because the images of the horses 
which impress themselves upon the eye are moving towards the centre 
of the surface of the pupil of the eye. 

K 120 [40] V. 


Foreshorten, on the summits and sides of the hills, the outlines of the 
estates and their divisions; and, as regards the things turned towards you, 
make them in their true shape. tsir. 

Among things of equal velocity, that will appear of slower movement 
which is more remote from the eye. 

Therefore that will appear swifter which is nearer to the eye. 

B.M. 134 V. 

\Aerial perspecthe\ 

In the morning the mist is thicker up above than in the lower parts 
because the sun draws it upwards; so with high buildings the summit 
will be invisible although it is at the same distance as the base. And this 
is why the sky seems darker up above and towards the horizon, and does 
not approximate to blue but is all the colour of smoke and dust. 

The atmosphere when impregnated with mist is altogether devoid 
of blueness and merely seems to be the colour of the clouds, which turn 
white when it is fine weather. And the more you turn to the west the 
darker you will find it to be, and the brighter and clearer towards the 
east. And the verdure of the countryside will assume a bluish hue in 
the half-mist but will turn black when the mist is thicker. 

Buildings which face the west only show their illuminated side, the 
rest the mist hides. 

When the sun rises and drives away the mists, and the hills begin to 
grow distinct on the side from which the mists are departing, they 
become blue and seem to put forth smoke in the direction of the mists 
that are flying away, and the buildings reveal their lights and shadows; 
and where the mist is less dense they show only their lights, and where it 
is more dense nothing at all. Then it is that the movement of the mist 
causes it to pass horizontally and so its edges are scarcely perceptible 



against the blue of the atmosphere, and against the ground it will seem 
almost like dust rising. . 

In proportion as the atmosphere is more dense the buildings in a 
city and the trees in landscapes will seem more infrequent, for only the 
most prominent and the largest will be visible. 

And the mountains will seem few in number, for only those will be 
seen which are farthest apart from each other, since at such distances the 
increases in the density creates a brightness so pervading that the darkness 
of the hills is divided, and quite disappears towards their summits. In the 
small adjacent hills it cannot find such foothold, and therefore they 
are less visible and least of all at their bases. 

Darkness steeps everything with its hue, and the more an object is 
divided from darkness the more it shows its true and natural colour. 

B.M. 169 r. 

Equal things equally distant from the eye will be judged to be of 
equal size by this eye. 


The shaded and the illuminated parts of opaque bodies will be in 
the same proportion of brightness and darkness as are those of their 
objects [that is of the body or bodies which project upon them]. 

Forster ii 5 r. 


Of things of equal size that which is farther away from the eye will 
appear of less bulk. FonternTsv. 

0 F P E RS P E C T I V E 

When the eye turns away from a white object which is illuminated 
by the sun, and goes to a place where there is less light, everything there 
will seem dark. And this happens, because the eye that rests upon this 
white illuminated object proceeds to contract its pupil to such an 
extent that whatever the original surface that was visible they will have 
lost more than three quarters of it, and thus lacking in size they will 
also be lacking in power. 

Though you might say to me: — a small bird then would see in pro- 
portion very little, and because of the smallness of its pupils the white 
there would appear black. To this I should reply to you that we are 


here paying attention to the proportion of the mass of that part of the 
brain which is devoted to the sense of sight, and not to any other thing. 
Or — to return — this pupil of ours expands and contracts according to 
the brightness or darkness of its object, and since it needs an interval of 
time thus to expand and contract, it cannot see all at once when emerging 
from the light and going to the shade, nor similarly from the shade to 
what is illuminated ; and this circumstance has already deceived me when 
painting an eye, and from it I have learnt. ^ ^ 

Among equal things the more remote will seem the smaller; and the 
proportion of the diminutions will be as that of the distances. 

, Quaderni IV lo r. 

[Perspective of colour s\ 

Make the perspective of the colours so that it is not at variance with 
the size of any object, that is that the colours lose part of their nature in 
proportion as the bodies at different distances suffer loss of their natural 


Since walnuts are covered with a certain thin skin which derives its 
nature from the husk, unless you peel this off when you are making the 
oil this husk will tinge the oil, and when you use it in your work 
the husk becomes separated from the oil and comes to the surface of the 
picture, and this is what causes it to change. c a 4 v b 


Take rubies of Rocca Nera or garnets and mix with lattimoy^ also 
Armenian bole is good in part. Tr 71 a 

Sap of spurge and milk of the fig tree as a dissolvent. 

H 65 [17] r. 

You will make good ochre if you employ the same method that one 
uses to make white lead. - 

H 94 [46] V. 


Take cypress [oil] and distil it, and have a large jug and put the 
distilled essence in it with so much water as to make it the colour of 
amber, and cover it over well so that it does not evaporate; and when it 
has dissolved add in this jug of the said essence so that it shall be as 
liquid as you desire. And you must know that the amber is the latex of 
the cypress tree. 

And since varnish is the gum of juniper, if you distil the juniper 
the said varnish can be dissolved in this essence in the manner spoken of 

Forster. 43 r. 

Tap a juniper tree and water its roots, and mix the latex that exudes 
with oil of walnut and you will have perfect varnish made with varnish, 
and this same you will make from the cypress, and you will then have 
varnish of the colour of amber, beautiful and famous for its quality. 
Make it in May or April. 


Temper with a little wax and it will not flake. And this wax should 
be dissolved with water, so that after the white lead has been mixed this 

^ Lattimo, a substance which has the colour of milk, used by glaziers. Neri Art. V itr. 



water having been distilled may pass away in steam and the wax only 
remain, and you will make good points. But know that it is necessary 
for you to grind the colours with a warm stone. ^ ^ 


Seed of mustard pounded with oil of linseed. 

Forster in lo v. 

Make oil from seed of mustard, and if you wish to make it more 
easily mix the seed after grinding it with oil of linseed, and put it all 
under a press. Forster m 40 r. 


Paste [is made] of emery mixed with spirits of wine, or iron filings 
with vinegar, or ashes of walnut-leaves, or ashes of straw rubbed very 

The diamond is crushed [by being] wrapped up in lead and beaten 
with a hammer, the lead being several times spread out and folded up 
again, and it is kept wrapped up in paper so that the powder may not be 
scattered. Then melt the lead, and the powder rises to the surface of 
the lead when it has melted, and it is afterwards rubbed between two 

plates of steel so that it becomes a very fine powder; afterwards wash it 
with aqua fords and the black coating of the iron will be dissolved 
and will leave the powder clean. 

Lumps of emery can be broken up by placing them in a cloth folded 
many times and hitting it on the side with a hammer; and by this means 
it goes into flakes bit by bit and is then easily crushed; and if you place 
it on the anvil you will never break it on account of its size. 

The grinder of enamels ought to practise in this way upon plates of 

tempered steel with a steel press, and then place it in aqua fortis which 
dissolves all the steel that is eaten away and mingled with this enamel and 
makes it black, with result that the enamel remains purified and clean. 

If you grind it upon porphyry this porphyry is consumed and be- 
comes mingled with the enamel and spoils it, and aqua fortis will never 
free it from the porphyry because it cannot dissolve it. 

If you wish to make a beautiful blue, dissolve with tartar the 
enamel you have made and then take off the salt. 

Brass vitrified makes a fine red. n i ^ r 

Sul Volo Cover [i] v. 




‘Works of fame by which I could show to those 
who are to come that I have been.’ 

[Memorandum of order of events in the Battle of Anghiari, drawn up 
apparently for consultation by Leonardo in the composition of his pic- 
ture on the wall of the Council Chamber of the Palazzo della Signoria 
at Florence.] 

[Leadjers of the Florentines. 

Neri di Gino Capponi, 

Bernardetto de’ Medici. 

Niccolo da Pisa. 

Count Francesco. 


Pietro Gian Paolo. 

Guelfo Orsino. 

Messer Rinaldo degli Albizi. 

You should commence with the oration of Niccolo Piccinino to the 
soldiers and exiled Florentines, among whom was Messer Rinaldo degli 
Albizi. Then you should show him first mounting his horse in full 
armour and the whole army following him: forty squadrons of horse and 
two thousand foot soldiers went with him. 

And the Patriarch at an early hour of the morning ascended a hill 
in order to reconnoitre the country, that is the hills, fields and a valley 
watered by a river; and he saw Niccolo Piccinino approaching from 
Borgo San Sepolcro with his men in a great cloud of dust, and having 
discovered him he turned to the captains of his men and spoke with 

And having spoken he clasped his hands and prayed to God; and 
presently he saw a cloud, and from the cloud St. Peter emerged and 
spoke to the Patriarch. Five hundred cavalry were despatched by the 
Patriarch to hinder or check the enemy’s attack. 

In the foremost troop was Francesco, son of Niccolo Piccinino, and 
he arrived first to attack the bridge which was defended by the 
Patriarch [?]‘ and the Florentines. 

Behind the bridge on the left he sent the infantry to engage our men 
who beat off the attack. Their leader was Micheletto who [ . . . ] was 
IMS. has PP. 


the officer of the watch at the court. Here at this bridge there was a 
great fight: the enemy conquer and the enemy are repulsed. 

Then Guido and Astorre his brother, lord of Faenza, with many of 
their men, reformed and renewed the combat, and hurled themselves 
upon the Florentines with such vigour that they regained possession of 
the bridge, and pushed their advance as far as the tents. 

Opposite to these came Simonetto with six hundred cavalry to harass 
the enemy, and he drove them again from the spot and reoccupied the 

And behind him came another company with two thousand cavalry, 
and so for a long time the battle swayed. 

And then the Patriarch to throw disorder into the ranks of the enemy 
sent forward Niccolo da Pisa and Napoleone Orsino, a beardless youth, 
and with them a great multitude of men, and then was done another 
great deed of arms. 

And at this time Niccolo Piccinino pushed up another unit of his 
followers, and this caused yet another advance by our men; and had it 
not been for the Patriarch throwing himself into the midst and sustaining 
his commanders by words and deeds the enemy would have driven them 
in flight. 

And the Patriarch made them set up certain pieces of artillery on the 
hill, by means of which he spread confusion among the infantry of the 
enemy. And this disorder was so great that Niccolo began to call back 

his son and all his followers and they started in flight towards the Sorgo. 
And at this spot there occurred a great slaughter of men, and none 
escaped save those who were the first to fly or those who hid themselves. 

The passage of arms continued until the going down of the sun, and 
the Patriarch busied himself in withdrawing his troops and burying the 
dead, and afterwards he set up a trophy. 

. ^ ^ c.A. 74 r. b and 74 v. c 

T R I V U L Z I O^ 

Cost of the work and material for the horse 
A courser, life size, with the rider, requires for the cost of 
the metal ducats 500 

^ For a discussion of the evidence relating to the project for a sepulchral monument of 
Marshal Trivulzio of which this is an estimate, see the author’s Mtnd of Leonardo (Cape, 
1 928), pp. 336-9. 



And for the cost of the iron work which goes inside the 
model, and charcoal, wooden props, pit for the casting, 
and for binding the mould, including the furnace 
where it is to be cast 

For making the model in clay and afterwards in wax 

And for the workmen who polish it after it has been cast 


Cost of the marble for the tomb 

Cost of the marble according to the design. The piece of 
marble which goes under the horse which is 4 braccia 
long and 2 braccia 2 inches wide and 9 inches thick, 
58 hundredweight, at 4 lire 10 soldi per hundred- 

And for 1 3 braccia 6 inches of cornice, 7 inches wide and 

4 inches thick, 24 hundredweight 

And for the frieze and architrave which is 4 braccia 6 
inches long, 2 braccia wide and 6 inches thick, 20 

And for the capitals made of metal of which there are 8, 

5 inches square and 2 inches thick: at the price of 1 5 
ducats each they come to 

And for 8 columns of 2 braccia 7 inches, 4^ inches thick, 
20 hundredweight 

And for 8 bases, 5J inches square and 2 inches high 5 

And for the stone, where it is upon the tomb, 4 braccia 
10 inches long, 2 braccia 4-| inches wide, 36 hundred- 

And for 8 feet of pedestals, which are 8 braccia long, 
6| inches wide, 6| inches thick, and 20 hundredweight 

And for the cornice that is below, which is [ . . . ] braccia 
10 inches long, 2 braccia 5 inches wide and 4 inches 
thick, 3 2 hundredweight 

And for the stone of which the recumbent figure (il 
morto) is to be made, which is 3 braccia 8 inches long, 
I braccia 6 inches wide, 9 inches thick, 30 hundred- 

. 389. 

ducats 200 
ducats 432 
ducats 450 

ducats 1582 

ducats 58 
ducats 24 

ducats 20 

ducats 1 20 
ducats 20 
ducats 5 

ducats 3 6 
ducats 20 

ducats 3 2 

ducats 30 


And for the stone that is beneath the recumbent figure, 
which is 3 braccia 4 inches long, i braccia 2 inches 
wide, 4 J inches thick 

And for the slabs of marble interposed between the 
pedestalS) of which there are 8 — 9 braccia long, 9 
inches wide, 3 inches thick —8 hundredweight 


Cost of the work upon the marble 
Round the base of the horse there are 8 figures at 25 
ducats each 

And in the same base are 8 festoons with certain other 
ornaments, and of these there are 4 at the price of 1 5 
ducats each, and 4 at the price of 8 ducats each 
And for squaring these stones 

Further for the large cornice, which goes below the base 
of the horse, which is 13 braccia 6 inches at 2 ducats 
per braccio 

And for 1 2 braccia of frieze at 5 ducats per braccio 
And for 1 2 braccia of architrave at i J ducats per braccio 
And for 3 rosettes which form the soffit of the monument, 
at 20 ducats the rosette 
And for 8 fluted columns at 8 ducats each 
And for 8 bases at one ducat each 
And for 8 pedestals, of which there are 4 at 10 ducats 
each, which go above the corners, and 4 at 6 ducats each 
And for squaring and framing the pedestals at 2 ducats 
each, there being eight 

And for 6 tables with figures and trophies at 25 ducats 

And for making the cornices of the stone which is be- 
neath the recumbent figure 
For making the recumbent figure, to do it well 
For 6 harpies with candlesticks, at 25 ducats each 
For squaring the stone on which the recumbent figure 
rests, and its cornice 


ducats 1 6 






































i °75 



The total of everything added together is ducats 3046. 

The Labours of Hercules for Pier F. Ginori. 

The Garden of the Medici.^ 

[Diagram for Altarpiece\ 

C.A. 179 V. a 

C.A. 288 V. b 



San Piero 








San Francesco 

Our Lady 





Santa Chiara 



: ^1 

Antonio da Padua 


Antonio: lily and book. 

Bernardino: with Jesus. 

Lodovico: with three lilies on his breast, with crown at his feet. 

Bonaventura: with seraphim. 

Santa Chiara: with the tabernacle. 

Elisabetta: with queen’s crown. „ r , 

T 1 107 [59]^- 

^ From the juxtaposition of these two notes in the manuscript the first may perhaps be 
interpreted as a reference to an intended commission, probably for a work in sculpture, to be 
executed or studied for among the casts in that Garden of the Medici in the piazza di San 
Marco, where in the time of II Magnifico an Academy of the Arts existed under the charge 
of the sculptor Bertoldo. Its existence is referred to by Vasari in his lives of Donatello and 
Torrigiano. The fact of Leonardo having worked for a time in this garden is borne witness 
to in the short biography of him written just before the middle of the sixteenth century by 
a Florentine known as the Anonimo Gaddiano: 

‘He lived as a youth with Lorenzo de’ Medici II Magnifico who in order to make 
provision for him set him to work in the garden of the piazza of San Marco in Florence.’ 

® Following on his identification of the names at the head of the two lists as those 
of the two patron saints of Brescia, Dr. Emil Mdller has put forward reasons for regarding 

. . , ■ 391 : 


[Notes apparently relating to some commission^ 

Ambrogio de Predis. 

San Marco, 

Board for the window. 

Gaspari Strame. 

The saints of the chapel. 

The Genoese at home. 

L I r. 

[Note with drawing — apparently of mechanism of stage scenery^ 

a h,c di%z hill which opens thus: a b goes to c ^ and c d goes to ef\ 
and Pluto is revealed in g^ his residence. 

When Pluto’s paradise is opened then let there be devils placed there 
in twelve pots to resemble the mouths of hell. 

There, there should be Death, the Furies, Cerberus, many nude Putti 
in lamentation. There fires made in various colours. .. . 

B.M. 231 V. 

[For heraldic devices — with dr awingsl 

A N T O N I O M A R I A 

On the left side let there be a wheel, and let the centre of it cover the 
centre of the horse’s hinder thigh-piece, and in this centre should be 
shewn Prudence dressed in red, representing Charity, sitting in a fiery 
chariot, with a sprig of laurel in her hand to indicate the hope that 
springs from good service. 

On the opposite side let there be placed in like manner Fortitude 
with her necklace in hand, clothed in white which signifies . . . and all 
crowned, and Prudence with three eyes. 

The housing of the horse should be woven of plain gold, bedecked 
with many peacocks’ eyes, and this applies to all the housings of the 
horse and the coat of the man. 

The crest of the man’s helmet and his hauberk of peacocks’ feathers, 
on a gold ground. 

Above the helmet let there be a half-globe to represent our hemi- 
sphere in the form of a world, and upon it a peacock with tail spread out 
to pass beyond the group, richly decorated, and every ornament which 

this sketch as intended for an altar-piece for S, Francesco at Brescia, which he believes to 
have been contemplated by Leonardo in the year 1479. (See Repertorium fur Kunstwissen- 


belongs to the horse should be of peacocks’ feathers on a gold ground, 
to signify the beauty that results from the grace bestowed on him who 
serves well. 

In the shield a large mirror to signify that he who really wishes for 
favour should be mirrored in his virtues. 250 r. 


Count Giovanni, of the household of the cardinal of Mortaro. 

Giovannina, face of fantasy; lives at Santa Caterina at the hospital. 

Forster ii 3 r, 

Alessandro Carissimo of Parma for the hand of Christ. „ ^ . 

r orster u o r. 

One who was drinking and left the cup in its place and turned his 
head towards the speaker. 

Another twists the fingers of his hands together and turns with stern 
brows to his companion. 

Another with hands opened showing their palms raises his shoulders 
towards his ears and gapes in astonishment. 

Another speaks in the ear of his neighbour, and he who listens turns 
towards him and gives him his ear, holding a knife in one hand and in 
the other the bread half divided by this knife. 

Another as he turns holding a knife in his hand overturns with this 
hand a glass over the table. 

Another rests his hands upon the table and stares. 

Another breathes heavily with open mouth. 

Another leans forward to look at the speaker and shades his eyes with 
his hand. 

Another draws himself back behind the one who is leaning forward 
and watches the speaker between the wall and the one who is leaning. ^ 

Forster n 62 V. and 63 r. 

Cristofano da Castiglione lives at the Pieta, he has a fine head. 

Forster in i v. 

The Florentine morel of Messer Mariolo, a big horse, has a fine 
neck and a very fine head. ® 

^ Description of action of figures in ‘The Last Supper’. 

® MS. Morel fiorentino di miser Mariolo. Morel, a dark-coloured horse (Murray). 
As the manuscript in which these notes occur bears references to the years 1493 ^^* 1 , H 94 
they may refer to studies for the equestrian statue of which a model was erected in the 
latter year. 


White stallion belonging to the falconer has fine haunches, is at the 
Porta Comasina. 

Big horse of Cermonino belongs to Signor Giulio. Forster m 88 r 

[With drawing of foreleg with measurements^ 

The Sicilian of Messer Galeazzo. 

Make this the same within, with the measure of all the shoulder. 

Windsor: Drawings 12294 

\With drawing of horse\ 

The big iennet of Messer Galeazzo. w j • 

o •' Windsor: Drawings 1 23 1 9 

[These verses, presumably sent to Leonardo by an admirer of his 
art, are the evidence of his having painted a portrait of Lucrezia Crivelli, 
a lady of the Milanese Court] 

Ut bene respondet naturae ars docta: dedisset 
Vincius, ut tribuit cetera, sic animam. 

Noluit, ut similis magis haec foret: altera sic est: 

Possidet illius Maurus amans animam. 

Hujus, quam cernis, nomen Lucretia: divi 
Omnia cui larga contribuere manu. 

Rara huic forma data est: pinxit Leonardos: amavit 
Maurus: pictorum primus hie: ille ducum. 

Naturam et superas hac laesit imagine divas 

Pictor: tantum hominis posse manum haec doluit. 

Illae longa dari tarn magnae tempora formae: 

Quae spatio fuerat deperitura brevi. 

Has laesit Mauri causa: defendet et ipsum 

Maurus: Maurum homines laedere diique timent.^ 

C.A. 167 v.',c ' 

^ How well the master’s art answers to nature. Da Vinci might have shown the 
soul here, as he has rendered the rest. He did not, so that his picture might be the 
greater likeness; for the soul of the original is possessed by II Moro, her lover. 

This lady’s name is Lucrezia, to whom the gods gave all things with lavish hand. 
Beauty of form was given her: Leonardo painted her, II Moro loved her — one the 
greatest of painters, the other of princes. 

By this likeness the painter injured Nature and the goddesses on high. Nature 
lamented that the hand of man could attain so much, the goddesses that immortality 
should be bestowed on so fair a form, which ought to have perished. 

For II Moro’s sake Leonardo did the injury, and II Moro will protect him. Men 
and gods alike fear to injure II Moro. 

■ 394 - ■ ■ 



‘As practising myself the art of sculpture no less 
than that of painting, and doing both the one and 
the other in the same degree.’ 

■» 1 

\Notes made in preparation for a statue\ 

Of that at Pavia 1 the movement more than anything else is deserving 
of praise. 

It is better to copy the antique than modern work. 

You cannot combine utility with beauty as it appears in fortresses 
and men. 

The trot is almost of the nature of the free horse. 

Where natural vivacity is lacking it is necessary to create it for- 


The sculptor cannot represent transparent or luminous things. 

C.A. 215 V. d 

All the heads of the large iron pins.® ca 216 v a 

How the eye cannot discern the shapes of bodies within their 
boundaries except by means of shadows and lights; and there are many 
sciences which would be nothing without the science of these shadows 
and lights: as painting, sculpture, astronomy, a great part of perspective 
and the like. 

As may be shown, the sculptor cannot work without the help 
shadows and lights, since without these the material carved would remain 
all of one colour; and by the ninth of this [book] it is shown that a level 
surface illumined by uniform light does not vary in any part the clear- 
ness or obscurity of its natural colour, and this uniformity of colour goes 
to prove the uniformity of the smoothness of its surface. It would follow 
therefore that if the material carved were not clothed by shadows and 
lights, which are necessitated by the prominences of certain muscles and 
the hollows interposed between them, the sculptor would not be able un- 
interruptedly to see the progress of his own work, and this the work that 

^ The reference is to the antique bronze equestrian statue representing Odoacer, King of 
the Goths, according to the Anonimo Morelliano, Gisulf according to Antonio Campo the 
historian of Cremona, which was removed by Charlemagne from Ravenna to Pavia and 
stood in the Piazza del Duomo until the time of its destruction, which occurred in a 
revolutionary outbreak in 1796. It was called Regisole, the name being derived from the 
reflections of the sun’s rays on the gilded bronze. Petrarch in a letter to Boccaccio says of it 
that ‘it was looked upon as a masterpiece of art by all good judges’. 

® The words are at the side of a drawing in red chalk representing a horse in an attitude 
of walking seen within a frame. 



he is carving requires, and so what he fashioned during the day would 
be almost as though it had been made in the darkness of the night. 

o F P A I N T I N G 

Painting, however, by means of these shadows and lights comes to 
represent upon level surfaces scenes with hollows and raised portions, 
separated from each other by different degrees of distance and in 
different aspects. 

V C.A. 277 V. a 

Measurement of the Sicilian [horse], the leg behind, in front, raised 
and extended. 

c,A. 291 V. a 


If you wish to make a figure of marble make first one of clay, and 
after you have finished it and let it dry, set it in a case, which should be 
sufficiently large that ~ after the figure has been taken out —■ it can hold 
the block of marble wherein you purpose to lay bare a figure resembling 
that in clay. Then after you have placed the clay figure inside this case 
make pegs so that they fit exactly into holes in the case, and drive them 
in at each hole until each white peg touches the figure at a different spot; 
stain black such parts of the pegs as project out of the case, and make a 
distinguishing mark for each peg and for its hole, so that you may fit 
them together at your ease. Then take the clay model out of the case 
and place the block of marble in it, and take away from the marble 
sufficient for all the pegs to be hidden in the holes up to their marks, 
and in order to be able to do this better, make the case so that the whole 
of it can be lifted up and the bottom may still remain under the marble; 
and by this means you will be able to use the cutting tools with great 

A 43 r. 


Because the time of the blow is indivisible, like the contact caused by 
this blow, its operation is of such swiftness that time does not permit this 
blow to transfer itself to the foundations of the things struck with suffi- 
cient swiftness to prevent the blow being already dead in its upper parts, 
like the mason who breaks a stone in his hand with a hammer without 
violence or damage to the hand. 

And this is why, after the iron a b has been struck by the blow of the 


hammer in its upper part this part has obeyed the nature of the blow 
rather than transferred it to its base so that the extremity is enlarged 
more than the base. 

And from this it follows that sculptors work to better effect upon 
their marbles when they rough-hew with a pointed hammer than with 
a chisel struck by the hammer. 

A sharp sword will also cut a roll in the air. ^ ^ ^ 


When you have finished building up the figure you will make the 

statue with all its surface measurements. ^ • 

C^uaderni ni 3 r. 

Some have erred in teaching sculptors to surround the limbs of their 
figures with wires, as though believing that these limbs were of equal 
roundness at each part at which they were surrounded by these wires. 

Quaderni vi 10 r. 



‘Of the horse I will say nothing because I know 
the times.’ 

... the cold will have sufficient thickness to touch the plaster, and 
you pour out the rest and fill with plaster and then break the mould, and 
put the iron pins across, boring through the wax and plaster, and then 
clean the wax at your leisure; afterwards put it in a case, and put a mould 
of plaster over it, leaving the air holes and the mouth for the casting. 
Through this mouth turn the mould upside down, and after it has been 
heated you will be able to draw out the wax contained within it; and you 
will be able to fill up the vacuum which remains with your liquified 
material, and the thing cast will become hollow. But in order to prevent 
the plaster from becoming broken while being rebaked you must place 
within it what you know of. 

C.A. 352 r. c 

\With drawing of apparatus] 

This is the way in which the forms rapidly dry and are continually 
turned like roasts, 

1 r. 29 a 


You should make a bunch of iron wire as thick as fine string and 
scrub them with it with water, but keeping a tub beneath so that it may 
not cause mud below. 


You should make an iron rod which may be of the shape of a large 
chisel, and rub it along the edges which remain upon the casts of the 
guns and which are caused by the joins in the mould; but see that the 
rod is a good weight and let the strokes be long and sweeping. 


First alloy part of the metal in the crucible and then put it in the 
furnace: this being in a molten state will make a beginning in the melting 
of the copper. 

TO G U A R D A G A I N S T T H E C O P P E R C 0 O L I N G 

When the copper begins to cool in the furnace proceed instantly as 


soon as you see this to slice it up with a stirring pole while it is in a paste, 
or if it has become entirely cold, cut it as you would lead with broad large 


If you have to make a cast of a hundred thousand pounds, make it 
with five furnaces with two thousand pounds for each, or as much as 
three thousand pounds at most, ^ 


The board that serves as a guide to the shape of the mortar ought 
therefore to be reduplicated from the centre backwards by the breadth 
of a great plank, to the end that it should not become twisted, and where 
this board has the impress of the frames and form of the cannon is the 
face not the edge, and when you add the tallow burnish this face with 
a pig’s tooth so that it may be solid, and let the tallow be finely strained 
in order that as it turns it may not make marks. 


If you wish to break a large mass of bronze suspend it first, then make 
a wall round it on the four sides in the shape of a hod for bricks, and 
make a great fire there; and when it is quite red-hot give it a blow with a 
great weight raised above it and do this with great force. 

\With two sketches^ 



Make the courses for the bronze as is shown here just now; and keep 
d b c stopped up, but leave the course a entirely open; and when that is 
full unstop and when that is full unstop c, and then d\ and the door of 
the courses should be of brick, the thickness of three fingers and well 
covered with ashes and then it is opened with the pincers; and branches 
of the courses when they also are cast ought to be divided with small 
plates of iron covered with earth before they are fastened. 

404,-.. . ■ 

Tr, 48 a 


O T H E R M E T A L 

If you wish for the sake of economy to put lead with the metal, and 
in order to lessen the amount of the tin which is necessary, first alloy 
the lead with the tin and then put above the molten copper. 


The furnace should be between four pillars with strong foundations. 


The coating ought not to exceed the thickness of two fingers, and it 
ought to be laid on in four thicknesses over the fine clay and then well 
prepared, and it should be annealed only on the inside and then given 
a fine dressing of ashes and cattle dung. 


The mortar ought to carry a ball of six hundred pounds and more, 
and by this rule you will take the measure of' the diameter of the ball 
and divide it in six parts, and one of these parts will be its thickness at 
the muzzle, and it will always be half at the breech. And if the ball is 
to be of seven hundred pounds one seventh of the diameter of the ball 
will be its thickness at the muzzle, and if the ball is to be eight hundred 
it will be the eighth of its diameter at the muzzle, and if nine hundred 
one eighth and one half of it, and if one thousand one ninth. 


If you wish it to throw a ball of stone, make the length of the tube 
as six or up to seven times the diameter of the ball; and if the ball is to 
be of iron make this tube up to twelve times the ball, and if the ball is 
to be of lead make it up to eighteen times. I mean when the mortar is 
to have its mouth fitted to receive within it six hundred pounds of stone 
ball and over. 


The thickness of small cannon at the muzzle ought not to exceed 
from a third to a half of the diameter of the ball, nor the length from 
thirty to thirty six times its diameter. ^ 



The furnace ought before you put the metal in it to be luted with 
earth from Valenza, and over that ashes. 

P O I N T O F C O O L I N G 

When you see that the bronze is on the point of becoming congealed 
take wood of the willow cut into small chips and make up the fire with it. 


I say the cause of this congealing is often derived from there being 
too much fire and also from the wood being only half-dried. 


You will know when the fire is good and suitable by the clear flames, 
and if you see the points of these flames turbid and ending in much 
smoke do not trust it, and especially when you have the molten metal 
almost in fluid state. 


Wood is suitable when it is the young willow, or if willow cannot be 
procured get alder, and let each branch be young and well dried. 

The metal used for bombards must invariably be made with six or 
even eight parts to a hundred, that is six parts of tin to one hundred of 
copper, but the less you put in the stronger will be the bombard. 


The tin should be put with the copper when you have the copper 
changed into a fluid state. 


You can expedite the process of melting when the copper is two- 
thirds changed to a fluid state. With a chestnut rod you will then be 
able frequently to manage to stir the remainder of the copper which is 
still in one piece amid the melted part. ^ ^ 



Take the dust of wool clippings and fix it on a wall in thin plaster 
so that it dries well. Then pound it and sift in fine powder, and to fifty 
parts of this powder add ten parts of brick, not over-baked and well 
pounded and sifted, also a small quantity of fine wool clippings or fustian 
cloth; and then to this compound add six parts of ashes which you will 
sift when moistened with water well salted; and this you will apply 
liquid and thin two or three times with a plasterer’s brush, leaving it 
every time to dry without fire. Also it would be advisable to add first 
to this mixture ashes of burnt ox-dung moistened with salt water. 


The tallow ought to be applied mixed with soot from a black- 
smith, and as fine as you can, or if you desire ashes of ox-dung. 

o F T H E F R A M E S 

The frames should be made almost to the limit of the cord as though 
[one were winding] a peg-top, and above this the frames should be 
completed with fine earth and polished with the said tallow and soot, 
and the ornaments should be of wax. 

The frame of the tail ought to have as its final covering a square in 
which are brickdust and ashes with salt water. Or it is even better to 
apply ashes of ox-dung with salt water over the said frame. 


The frame should first be put in the trench with grappling-hooks as 
you saw before, then annealed little by little, emerging in the manner 
somewhat of the colour of brick (di poi lau [.?] con uno negnietto) 
striking softly bit by bit, and where you hear it resound bind with 
iron wire, but in order not to go astray place it to turn everywhere. 


The earth to be generally used ought to be that of which bricks are 
made, mixed with ox-dung or clippings of woollen cloth. ^ 



The bottom of the stove, three rows of unbaked bricks of ordinary 
clay and an inch and a half of ashes, the vault one layer of unbaked 
bricks of Valenza clay and another layer of baked bricks. 

Loose earth [?] ^ should be put with the ashes. 

The wood of the frame of the bombards should be covered an inch 
deep in cinders. 

The mouth of the stove, that is where the flame enters, ought to be of 
large bricks of Valenza clay. 

Each of two flues ought to be for the half of the window for the 
entrance of the flame. rp 

NOTES o N U S E O F ‘ S A G O M A ’ ^ 

Let the plumb-line be extended in two directions opposite to the 
centre of the poles a c, and let the plane surface be formed of plaster 
(MS. osseg— gesso) little by little under the movement of the ‘sagomak 

And when the pavement is entirely finished the whole should be 
corrected again minutely with the ‘sagoma’; and this ‘sagoma’ when 
used on the prepared otasseg-gessato) should be used 

with the greatest possible care. ci+r 

[Of friction of the sagomd\ 

The friction of the polishing instrument against its surface ought 
not to be done with the edge of the instrument, except when first pre- 
paring the said surface. But when it is necessary to refine this surface 
then the instrument ought not to be of less width than half the surface. 
This may be proved: suppose jf e d c to the said polishing instrument 
and f e n m tho smoothed surface. I maintain that if this polishing 
instrument were to have only one cutting edge, as in ^ c with a b, it 
would have far greater weight when the perpendicular line was upon 
the part d c Q^ the smoothed surface than when it was on the position 
f e o^ the said surface. And for this reason it would wear away the rubbed 
parts much more if it were straight than if it were slanting. And the 
concaveness of this surface would be unequal, such inequality as cannot 

^ MS. i colossi 

Hoare’s Ital. Diet, art, loscto has terra loscta, loose earth. 

® A mould, also ‘an instrument for smoothing and polishing a surface’ — Ravaisson- 



be formed by the great contact of the polishing instrument with the 
surface which it polishes. 

But it would be better that the instrument and the surface should 
be the equal the one of the other, for when one of the sides of the instru- 
ment was in the middle of the said surface its extremity would receive 
all the accidental weight of this instrument. 

But the polishing instrument with one cutting edge is necessary, 
merely in order to give the form to its smoothed surface by means of 
three or four movements, which should make it entirely perfect. 

G i6 r. 

The cogs that cause the movement of the sagoma set in their 

The sagoma should be as that used on the road of Fiesole — with 

Because it is necessary that in proportion as the said instrument is 
lowered so it wears itself away, and as after having been lowered it 
becomes very strong it is therefore necessary to make the pulleys with 
nuts so that screws turn within them, and that it shuts and opens between 
r as b shows between a c, and that these rings which form nuts for the 
screws should be drawn with the cords d ef g. ^ ^ 


Mercury with Jupiter and Venus: after the paste has been made it 
should be worked upon with the sagoma continually until Mercury is 
entirely separated from Jupiter and Venus. - 


Let the concavity be pressed with the instrument first several times 
backwards and forwards before it is varnished, then the varnish should 
be applied to the moist surface, and go over it with the sieve; use the 
mould two or three times, then expose it to the furnace, and when it 
acquires lustre immediately apply the mould while it is hot. 

The centre of the revolution of the mould upon the structure ought 
to be fixed, and such that it can be raised and lowered, and moved 
forward and backward, so that its . . . falls upon the centre of the mould. 

'^ Vernicu della igna. 

® i.e., according to Richter, quicksilver with iron and copper. 


Tlie base of the oven should be of the same shape as that of the 
object placed in the oven; and it is well that it should be of one piece of 
tufa stone, so that it can resist like an anvil the transverse percussion of 
the heavy mould which strikes it. 

J G 47 r. 

Let the wood of the sagoma be well covered over with pitch 
(MS. otaicepni-inpeciato) so that it may not bend. ^ ^ ^ 

In the polishing instrument there is a space left in order to be able 
to insert the lead moulding, and so that one may be able to change these 
from time to time as they are consumed. And so with the emery, one 
will guide the ‘male’ of the fired surface to perfection, and upon this 
one will afterwards print the copper (MS. emar = rame) after it has been 
made absolutely smooth. 

iV, surface, is of Saturn^ and it serves for the process of smoothing 
conjoined with the motive power, m below, in margin. 

The motive power is Neptune. 

This will keep the object to be polished below and the polishing 
instrument above; and the pole will find itself above, and so this pole 
not being weighed down as is that of the instrument represented above 
will come to maintain itself, and as it is not able to consume itself the 
process will be complete. 

Moreover the thing polished will support above itself the substance 
which polishes it, and the polishing instrument being of lead may be 
recast and adjusted many times. 

The mould may be of Venus, Jupiter or Saturn, and often cast back 
into the lap of its mother, and it may be worked over with fine emery; 
and the mould may be of Venus and Jupiter plastered over Venus. 

But first you will put to the test Venus and Mercury mixed with 
Jupiter, and manage so that Mercury may escape, and then roll them up 
tightly so that Venus and Jupiter become blended in Neptune as thinly 
as possible. 


This ought to be upside down, in order that the mould may weigh 
upon the surface it treats with a perpendicular weight. Thus the centre 
of the object in circumvolution will not consume itself, in order not to 
^ Lead, Richter. 



have the weight upon itself; and apart from this the polishing process 
will serve to receive and support it, as I have said in the first instance. 

G S3 r. 

Have a frame of stout walnut wood upon which build a square frame 
with raised centering, and upon this are fixed both ends of the drawn 
plate, which is separated at the end from the sides of the wall, carrying 
and holding with it all the plates that are nailed above. And this frame 
should always be with the above-mentioned dark plates. 


Cover with stucco the boss of the . . . (tngneaT) of plaster, and let 
this be made of Venus and Mercury^ and smear this boss well over with 
a uniform thickness of the blade of a knife, doing it with a rule (sagoma?) 
and cover this with the body of a bell so that it may drip, and you will 
have again the moisture with which you formed the paste: dry the rest 
well and then fire it, and beat or burnish it with a good burnisher, and 
make it thick towards the side. 

Powder the glass to a paste with borax and water, and make stucco; 
then drain it off so as to dry it, then varnish it with fire so that it shines 

If you wish to make a large thin metal plate of lead, make a smooth 
level surface and fill it with glowing coals and melt lead in it, and then 
with a smooth rake take away the coals and allow it to cool and it is 

Forster n 46 v. 

When you wish to cast in wax burn off the scum with a candle and 
the cast will come without holes. 

Grind verdigris with rue many times together with juice of lemon 
and keep it from Naples yellow. „ 

1 Ingnea, Venus and Mercury are written backwards in the text, i.e. they appear as 
aengni, erenev and oirucrem. Dr. Richter suggests that Venus and Mercury may mean 
‘marble’ and ‘lime’ of which stucco is composed. 

• ■■ . . 411 ... 


The steel is first beaten well for the length, then broken in squares, 
and these are placed one above another and well covered with earth 
of Valenza and powdered talc, and it is dried over a slow fire and 
gradually heated; and when it has been thoroughly heated both inside 
and out then the fire exerts its force and makes it become molten. But 
first insert flakes of iron, then have the earth gradually removed and 
beat it lengthwise; and this is good steel. ^ 

Dry earth sixteen pounds; a hundred pounds of metal; moistened 
earth twenty; moisten the hundred of metal which adds four pounds of 
water; one of wax, one pound of metal somewhat less; cloth clippings 
with earth measure for measure. Forster m 36 v. 

Two ounces of plaster to a pound of metal; [oil of] walnut eases it 
at the curve. Forster m 37 r. 


Take for every two cupfuls of plaster one of burnt ox-horn, and 
mix them together and make the cast. 

F O R C A s T I N G 

Tartar burnt and powdered with plaster and used in casting- 
causes such plaster to adhere together when it is annealed; then it is 
dissolved in water. Forster m +2 v. 

For mirrors, thirty of tin upon a hundred of copper; but first clarify 
the two metals and plunge them in water and granulate them, and then 
fuse the copper and put it upon the tin. ^ 


Make the horse upon legs of iron, strong and firm in a good founda- 
tion. Then rub it with tallow and give it a good coating, letting it dry 
thoroughly layer by layer. And by this you will increase its thickness 
by the breadth of three fingers. Then fix and bind it with iron accord- 
ing to need. Besides this hollow out the mould, then get it to the required 
thickness, and then fill up the mould again by degrees and continue 
until it is entirely filled. Then bind it round with its irons and strap it 
up, and anneal it on the inner side where it has to touch the bronze. 



Mark upon the horse when finished all the pieces of the mould with 
which you wish to cover the horse, and after the clay has been laid on 
cut it to correspond in every piece, so that when the mould is finished 
you can take it off and then replace it in its first position with its catches 
by the countersigns. 

The square block a h will go between the cover and the core, that is 
in the hollow space where the liquified bronze is to be; and these square 
blocks of bronze will keep the spaces between the mould and the cover 
at an equal distance, and for this reason these blocks are of great 

The clay must be mixed with sand. 

Take wax to give back and to pay for what has been used. 

Dry one layer after another. Make the outer mould of plaster in 
order to save time in drying and the cost of wood; and with this plaster 
fasten the iron bands outside and inside for a thickness of two fingers; 
make terra cotta. 

And this mould you will take a day to make; half a boat-load of 
plaster will serve you. 


Stop it up again with paste and clay, or white of egg and brick and 
rubble. Windsor : Drawings 12347 r. 

Three irons which bind the mould" 

If you wish to make casts rapidly and simply, make them with a box 
of river sand moistened with vinegar. 

After having made the mould upon the horse you will make the 
thickness of the metal in clay. 

Note in alloying how many hours are needed for each hundred- 
weight. In casting each keep the furnace with its fire closed up. Let all 
the inside of the mould be saturated with linseed oil or turpentine. Then 
take a handful of powdered borax and hard rosin with aqua vitae and 
put a coat of pitch over the mould so that while underground the damp 
may not [injure it?]. 

In order to manage the large mould make a model of the small 
mould; make a small room in proportion. 

Make the vents in the mould while it is upon the horse. 

" I have followed Richter’s order of arrangement in this passage. 


Hold the hoofs in tongs and cast them with fish-glue. 

Weigh the parts of the mould to find out what amount of metal it 
will take to fill them, and give so much to the furnace that it may 
supply each part with its quantity of metal; and this you will ascertain 
by weighing the clay of that part of the mould to which the quantity in 
the furnace has to correspond. And this is done so that the furnace that 
is for the legs fills them and does not have to supply metal for the head 
from the legs which would be impossible. 

Cast at the same casting as the horse the little door (sportello) of 

the .... Windsor; Drawings 12350 



‘If anyone wishes to go through the whole place 
by the high-level roads, he will be able to use 
them for this purpose, and so also if anyone 
wishes to go by the low-level roads.’ 

If the usual width of the river is that of one arch construct this 
Jge with three, and do this in order to allow for the floods. 

\Ground-plan of castle with lake and boats on it\ 

\T he palace of the prince ought to have a piazza infronty 

The rooms which you mean to use for dancing or to make different 
kinds of jumps or various movements with a crowd of people, should be 
on the ground floor, for I have seen them collapse and so cause the death 
of many. And above all see that every wall, however thin it may be, has 
its foundations on the ground or on well-planted arches. 

Let the mezzanines of the dwellings be divided by walls made of 
narrow bricks, and without beams because of the risk of fire. 

All the privies should have ventilation openings through the thick- 
ness of the walls, and in such a way that air may come in through the 

Let the mezzanines be vaulted, and these will be so much the stronger 
as they are fewer in number. 

Let the bands of oak be enclosed in the walls to prevent them from 
being damaged by fire. 

Let the privies be numerous and be connected one with another, so 
that the smell may not spread through the rooms, and their doors should 
all close automatically. 

[Plans] Kitchens. Pantry. 

[Plan^ Kitchens. Stable. Eighty braccia wide and a hundred and 
twenty braccia long in ground plan. Combats by means of the boats, 
that is the combatants may be upon the boats. Ditch forty braccia. 
Road below. 

At the angle a should be the keeper of the stable. 

The largest division of the front of this palace is in two parts, that 
is the width of the court is half the length of the aforesaid front.^ a 76 v b 
[With plan] 

Stable for the Magnifico, for the upper part, one hundred and ten 
braccia long and forty braccia wide. 

[With plan] 

Stable for the Magnifico, for the lower part, one hundred and ten 
^ Words crossed out in MS. 



braccia long, and forty braccia wide, and it is divided into four rows for 
horses, and each of these rows is divided into thirty-two spaces, called 
intercolumnar, and each intercolumnar space has a capacity for two 
horses, between which is interposed a swing-bar. 

This stable therefore has a capacity for a hundred and twenty-eight 

C.A. 96 V. a 

\T own-planning 

Give me authority whereby without any expense to you it may come 
to pass that all the lands obey their rulers, who ... 

The first renown will be eternal together with the inhabitants of the 
city built or enlarged by him. 

Let the bottoms of the reservoirs which are behind the gardens be 
as high as the level of the gardens, and by means of discharge-pipes they 
will be able to bring water to the gardens every evening every time that 
it rises, raising the joint half a braccio; and to this let the senior 
officials be appointed. 

]Wtthplan\ Canal. Weir. Garden. 

And nothing is to be thrown into the canals, and every barge is to be 
obliged to carry away so much mud from the canal, and this is after- 
wards to be thrown on the bank. 

'\With plani Construct in order to dry up the canal and to clean the 
(lesser) canals. 

All people obey and are swayed by their magnates, and these 
magnates ally themselves with and are constrained by their lords in 
two ways, either by blood-relationship or by the tie of property; blood- 
relationship when their sons, like hostages, are a surety and a pledge 
against any suspicion of their faith; the tie of property when you let 
each of them build one or two houses within your city, from which he 
may draw some revenue; and \in addition to he will draw from ten 
cities of five thousand houses with thirty thousand habitations, and you 
will disperse so great a concourse of people, who, herding together like 
goats one upon the back of another filling every part with their stench, 
sow the seeds of pestilence and death. 

And the city will be of a beauty equal to its name, and useful to you 
for its revenues and the perpetual fame of its growth. 

The municipality of Lodi will bear the expense, and keep the 
revenue which once a year it pays to the Duke. 

^ Words crossed out in MS. 

'418 ' , . 


To the stranger who has a house in Milan it will often befall that in 
order to be in a more imposing place he will go and live in his own 
house; and whoever is in a position to build must have some store of 
wealth, and in this way the poor people will become separated by such 
settlers, and when these . . . assessments will increase and the fame of its 
greatness. And even if he should not wish to reside in Milan he will 
still remain faithful, in order not to lose the profit of his house at the same 
time as the capital. ^ u 

\Archltectural drawings: ground plans\ 

Buttery. Kitchen. Family. 

He who is stationed in the buttery ought to have behind him the 
entrance to the kitchen, in order to be able to do his work expeditiously; 
and the window of the kitchen should be in the front of the buttery so 
that he may extract the wood. 

The drawing that I have made has a larger fagade behind than in 
front, whereas it should be the opposite. 

The large room for the family away from the kitchen, so that the 
master of the house may not hear their clatter; and the kitchen may be 
convenient for washing the pewter so that it may not be seen being 
carried through the house. 

Large room for the master. Room. Kitchen. Larder. Guard 
Room. Large room for the family. 

Larder, logs, kitchen and hen-coop {}pollaro) and hall, and the 
apartment will be or ought to be in contact for the convenience that 
ensues; and the garden and stable, manure and garden, in contact. The 
large room for the master and that for the family should have the kitchen 
between them, and in both the food may be served through wide and 
low windows, or by tables that turn on swivels. 

The wife should have her own apartment and hall {sala) apart from 
that of the family, so that she may set her serving-maids to eat at another 
table in the same hall. She should have two other apartments as well as 
her own, one for the serving-maids the other for the wet nurses, and 
ample space for their utensils. 

I wish to have one door to close the whole house. ck, 158 V. a 

The hall for the festival should be situated so that you come 
first into the presence of the lord, and then of the guests, and the passage 


should be so arranged that it enables you to enter the hall without 
passing in front of the people more than one may wish; and over on the 
other side opposite to the lord should be situated the entrance of the 
hall and a convenient staircase, which should be wide, so that the people 
in passing along them may not push against the masqueraders and 
damage their costumes, when going out ... the crowd of men . . . with 
such masks . . . this hall . . . two rooms side by side . . . right double . . . 
of this an exit . . . collection and one for the masqueraders. 

c.A. 214 r. b 

\A plan for laying out a water-garden\ 

The staircase is one braccio and three quarters wide and it is bent 
like a knee, and altogether it is sixteen braccia with thirty two steps 
half a braccio wide and a quarter high; and the landing where the stair- 
case turns is two braccia wide and four long, and the wall which divides 
one staircase from the other is half a braccio; but the breadth of the 
staircase will be two braccia and the passage half a braccio wider; 
so that this large room will come to be twenty-one braccia long and 
ten and a half braccia wide, and so it will serve well; and let us make it 
eight braccia high, although it is usual to make the height tally with the 
width; such rooms however seem to me depressing for they are always 
somewhat in shadow because of their great height, and the staircases 
would then be too steep because they would be straight. 

By means of the mill I shall be able at any time to produce a current 
of air; in the summer I shall make the water spring up fresh and bubbling, 
and flow along in the space between the tables, which will be arranged 
thus [drawingl. The channel may be half a braccio wide, and there 
should be vessels there with wines always of the freshest, and other 
water should flow through the garden, moistening the orange trees and 
citron trees according to their needs. These citron trees will be perma- 
nent, because their situation will be so arranged that they can easily be 
covered over, and the warmth which the winter season continually 
produces will be the means of preserving them far better than fire, 
for two reasons: one is that this warmth of the springs is natural and is 
the same as warms the roots of all the plants; the second is that the fire 
gives warmth to these plants in an accidental manner, because it is 
deprived of moisture and is neither uniform nor continuous, being 
warmer at the beginning than at the end, and very often it is overlooked 
through the carelessness of those in charge of it. 

. ■ .420 : 


The herbage of the little brooks ought to be cut frequently so that 
the clearness of the water may be seen upon its shingly bed, and only 
those plants should be left which serve the fishes for food, such as water- 
cress and other plants like these. 

The fish should be such as will not make the water muddy, that is to 
say eels must not be put there nor tench, nor yet pike because they 
destroy the other fish. 

By means of the mill you will make many water-conduits through the 
house, and springs in various places, and a certain passage where, when 
anyone passes, from all sides below the water will leap up, and so it will 
be there ready in case anyone should wish to give a shower-bath from 
below to the women or others who shall pass there. 

Overhead we must construct a very fine net of copper which will 
cover over the garden and shut in beneath it many different kinds of 
birds, and so you will have perpetual music together with the scents of 
the blossom of the citrons and the lemons. 

With the help of the mill I will make unending sounds from all 
sorts of instruments, which will sound for so long as the mill shall 
continue to move. 

C.A. 271 V. a 

\T he dimensions of a temple\ 

You ascended by twelve flights of steps to the great temple, which is 
eight hundred feet in circumference and is built in the shape of an 
octagon. At the eight corners were eight large plinths a braccio and a 
half in height and three in width and six in length at the base, with an 
angle in the centre which served as the foundation for eight large 
pillars that rose to a height of twenty-four braccia above the base of the 
plinth, and on top of these stood eight capitals three braccia each [in 
length] and six wide. Above these followed architrave, frieze and cornice, 
four braccia and a half in height, carried on in a straight line from one 
pillar to another, and thus it surrounded the temple with a circuit of 
eight hundred braccia; between each of the pillars, as a support to this 
entablature, there stood ten large columns of the same height as the 
pillars, three braccia thick above their bases which were one braccio and 
a half in height. 

You ascended to this temple by twelve flights of steps, the temple 
being upon the twelfth, built in the shape of an octagon, and above each 
angle rose a large pillar, and between the pillars were interposed ten 


columns of the same height as the pillars, which rose twenty-eight and a 
half braccia above the pavement. At this same height were placed 
architrave, frieze and cornice, which formed a circuit round the temple, 
eight hundred braccia in length and of uniform height. Within this 
circuit at the same level towards the centre of the temple at a distance of 
twenty-four braccia rise pillars and columns, corresponding to the eight 
pillars of the angles and the columns placed in the facade. And they 
rise to the same height as those already mentioned, and above these 
pillars the continuous architrave goes back towards the pillars and 
columns first spoken of. aSe r c 

Our ancient architects or such . . . commencing first of all with the 
Id, who according to the discourses of Diodorus Siculus were the first 
builders and constructors of great cities, and of fortresses and buildings 
both public and private which had distinction, nobility and grandeur; 
and by reason of this their predecessors beheld with amazement and 
stupefaction the lofty and immense engines which seemed to them . . . 

C.A. 3^5 r. b 

An inverted arch is better for making a support than an ordinary 
one, because the inverted arch finds a wall below it which resists its 
weakness, while the ordinary arch finds where it is weakest nothing but 


An arch is nothing other than a strength caused by two weaknesses; 
for the arch in buildings is made up of two segments of a circle, and 
each of these segments being in itself very weak desires to fall, and as 
the one withstands the downfall of the other the two weaknesses are 
converted into a single strength. 


When once the arch has been set up it remains in a state of equi- 
librium, for the one side pushes the other as much as the other pushes it; 
but if one of the segments of the circle weighs more than the other the 
stability is ended and destroyed, because the greater weight will subdue 
the less. 



^With architectural drawing and plan\ 

Ground plan of the pavilion which is in the middle of the labyrinth 
of the duke of Milan. 

Pavilion of the garden of the duchess of Milan. ^ 

[With plan and drawing of fortification^ 


With this square bastion you should make only two towers in order 
that having . . . that one may not impede the other; and at each tower 
you should make a bridge entering into the ravelin as is shown in the 
drawing. The diameter of the square bastion should be a hundred 
braccia, and the diameter of each tower should be thirty braccia. 

The ravelins should be open within so that being so the enemy cannot 
maintain himself there, but is exposed to attack from the towers. 

B 12 r. 

[With architectural drawing]^ 

If you have your family in your house, make their habitations in 
such a way that at night neither they nor the strangers to whom you 
give lodging are in control of the egress of the house; in order that they 
may not be able to enter in the habitation where you live or sleep, close 
the exit m. and you will have closed the whole house. 

•' B 12 V. 

\JVith drawing of section of wall of a house'\ 

C is a stove which receives heat from the kitchen chimney by means 
of a copper flue two braccia high and one wide, and a stone is put 
over the place in summer in order that it may be possible to use the 
stove; b will be the place for keeping salt, and at the division a there will 
be an opening of a passage into the chimney for hanging up salted meats 
and such like things; and in the ceiling there will be many flues for the 
smoke, with different exits at the four sides of the chimney, so that if 
the north wind should begin to be troublesome the smoke may find an 
outlet on the other side. And the smoke proceeds to spread itself through 
the numerous flues and to cure salted meats; tongues and sausages and 
things like these it brings to perfection. But see to it that when you push 
the small door a a window opposite opens, which gives light to the little 

’■ A document recently found at Como bearing the date March a8, I49®> consists of a 
contract for the supply of stone for a pavilion which ‘Maestro Lionardo painter and 
architect’ was to construct in Milan, 



room; and this will be done by means of a rod joined to the door and the 
window in this way, b 14 v 

\With ground plan of fortressl 

A way of a fortress with double moat. And the spurs which pass 
from the principal wall to the Garland serve two uses: that is they form a 
buttress and they help in part to render it possible to defend the base of 
the Garland when the principal wall has been thrown down. ^ ^ 

[Note with plan of section of town showing high- and low-level roads\ 

The roads [marked] m are six braccia higher than the roads [marked] 
p r, and each road ought to be twenty braccia wide and have a fall of 
half a braccio from the edges to the centre. And in this centre at every 
braccio there should be an opening one braccio long and of the width 
of a finger, through which rain-water may drain oflF into holes made at 
the level of the roads/ r. And on each side of the extremity of the width 
of this road there should be an arcade six braccia broad resting on 
columns. And know that if anyone wishes to go through the whole 
place by the high-level roads, he will be able to use them for this purpose, 
and so also if anyone wishes to go by the low-level roads. 

The high-level roads are not to be used by waggons or vehicles such 
as these but are solely for the convenience of the gentlefolk. All carts 
and loads for the service and convenience of the common people should 
be confined to the low-level roads. 

One house has to turn its back on another, leaving the low-level road 
between them. The doors n serve for the bringing in of provisions such 
as wood and wine and suchlike things. The privies, the stables and such- 
like noisome places are emptied by underground passages, situated at a 
distance of three hundred braccia from one arch to the next, each passage 
receiving its light through the openings in the streets above. And at 
every arch there should be a spiral staircase; it should be round because 
in the corners of square ones nuisances are apt to be committed. At the 
first turn there should be a door of entry into the privies and public 
urinals, and this staircase should enable one to descend from the high- 
level to the low-level road. 

The high-level roads begin outside the gates, and when they reach 
them they have attained a height of six braccia. The site should be 

. 424 ■ 


chosen near to the sea or some large river, in order that the impurities 
of the city which are moved by water may be carried far away. 

B i6 r. and 15 v. 


The earth which is dug out from the cellars ought to be raised at 
one side so as to construct a terrace garden at the same level as the hall; 
but see that between the earth of the terrace garden and the wall of the 
house there is an intervening, space, so that damp may not spoil the 
principal walls. B19V. 

UVith drawing and ground plan of churcK\ 

This edifice is inhabited both in the upper and in the lower part. 
The entrance to the upper part is by way of the campaniles, and it goes 
along the level on which rest the four drums of the dome, and the said 
level has a parapet in front of it. And none of these drums communicates 
with the church but they are entirely separate. ^24. r. 

Let the street be as wide as the universal height of the houses. 

■ ' B 36 r. 

[Castle of Milani 

[With drawing} ^ y . . .. 

The moats of the castle of Milan within the Garland are thirty 
braccia; the ramparts are sixteen braccia high and forty wide, and this 

is the Garland. ; ^ _ . 

The outer walls are eight braccia thick and forty high, and the inner 
walls of the castle are sixty braccia, which would please me entirely if it 
were not that I should wish to see that the bombardiers who are in the 
walls of the Garland do not issue forth in the secret inner way, that is in 
S, but lower themselves one at a time as appears in mf ^ 

Since good bombardiers always aim at the embrasures of fortresses, 
and can if they break a single embrasure in the said Garland enter like 
cats through this breach and make themselves masters of all the towers, 
walls, and secret passages of the Garland, therefore if the embrasures 
are w/and it shall come about that a mortar bursts one of these ^f^^ra- 
sures and the enemy enters within, they will not be able to pass farther 
but may be beaten back and driven away by a soldier stationed in the 
machicolations above; and the passage/ ought to be continued throug 
all the walls from three quarters downwards and without having any 

425 ' 


exit above, either in the walls or the towers, except that by which one 
enters, which will have its beginning within the fortress; and the above- 
mentioned secret passage jf ought not to have any air-hole on the outside 
but to get its light on the side of the fortress through the frequent 
loopholes. B36 v. 


\Witk drawing 

The way in which one should construct a stable: you will first divide 
its width in three parts, its length does not matter; and these three 
divisions should be equal, each being six braccia wide and ten high. 
The centre part should be for the use of the master of the stable, the 
two at the sides for the horses, each requiring for width three braccia 
and for length six braccia, and being half a braccio higher in front than 

The manger should be two braccia from the ground, the beginning 
of the rack three braccia, and the top of it four braccia. 

To attempt however to keep my promise, namely to make the said 
place contrary to the usual custom clean and neat: as to the upper portion 
of the stable, that is, where the hay is, this part should have at its outer 
end a window six [Pbraccia] high and six wide, by which hay can easily 
be brought up to the loft as is shown in the machine E; and this should 
be erected in a place six braccia in breadth and as long as the stable, 
as is shown in K p. The other two parts, which have the first between 
them, are each divided into two parts. The two towards the hay are four 
braccia, and are entirely for the use and passage of the stable attendants; 
the other two which extend to the outside walls are two braccia, as is 
shown in S Ry and these are for the purpose of giving the hay to the 
manger, by means of funnels narrow at the top, and broad above the 
mangers, so that the hay may not be stopped on the way. They should 
be well plastered and cleaned, as they are represented where it is marked 
4jf r. In order that the horses may be given water the troughs should be 
of stone, so made as to be able to be uncovered as are boxes by raising 
their lids. 


A building ought always to be detached all round in order that its 
true shape can be seen. 

■ B 39 V. 


B 39 V. 


[Drawing of castle showing staircases^ 

Here are five staircases with five entrances; and one is not visible to 
another and when anyone is in one he cannot go into another; and it is a 
good system for those who are maintained there, in that it prevents them 
from mingling with each other, and being separated they will be ready 
for the defence of the tower: this can be either round or square. 


[With drawingl 

Ten spiral staircases round a tower. 

•T B 47 V. 

[With plan of ravelin'\ 

The ramparts placed in front of the doors of the ravelin should be 
solid, except for the winding staircase placed in the centre in order to 
connect with the battlements above, and one enters into this staircase by 
subterranean passages. 

[With drawings^ 

A represents the upper church of San Sepolcro at Milan. 
B is the part of it below the ground. 

349 V 

3 57 r. 

[With drawingl 

Where you do not wish to have a portico round the whole of a 
courtyard, but that only one or two of the four sides should have the 
portico, make the others also with the same arrangement of columns, and 
surround the arches with an architrave on the inner side which descends 
as far as the bases of the columns. 

And make the windows within the said architraves, and in the same 
way place the chief beams within the rooms in such a manner as to 
come between one window and the other. ^ ^ 

[With drawing] 

Double staircase. One for the commander of the castle, the other 
for the garrison. b68v. 

Architraves of several pieces are stronger than those of merely one 
piece, if these pieces are so placed that their lengths point to the centre 
of the earth. This is proved from the fact that the stones have their 



marking, or vein, usually crosswise, that is in the direction of the opposite 
horizons of the same hemisphere, and this is the contrary to the vein, of . 
plants which have. ... g 52 r. 

[Of arch and support\ 

The continuous quantity bent by force into a curve pushes itself in 
the direction of the line into which it desires to return. h 35 v. 

That part of the continuous quantity will make a greater movement 
which is more distant from the part which moves less. 

That side of the support of which the upper part is the heavier 
will bend in a curve towards its centre. ^ ^6 v. 

The sides of every defined quantity which has been raised in a 
pyramidal heap will be of the slant of the angular diameter of the 
perfect square. h 37 r. 

[For decorating a room\ 

The narrow moulding at the top of the room — • thirty lire. 

For the moulding below this, I reckon each panel at seven lire, and, 
in expenses on azure, gold, white-lead, gypsum, indigo and size, 
three lire; time — three days. 

The subjects under these mouldings with their pilasters, twelve lire 
for each. 

I estimate the cost of enamel, azure and gold, and other colours at 
one lira and a half. 

I allow five days for studying the composition, the small pilaster 
and other things. 

Item for each small arch — seven lire. 

Cost of azure and gold — three and a half lire. 

Time — four days. 

For the windows — one and a half lire. 

The large cornice below the windows — sixteen soldi the braccio. 

Item for the Roman historical compositions — fourteen lire each. 

The philosophers — ten lire. 

The pilasters — one ounce of azure, ten soldi. 

For gold — fifteen soldi. 

I estimate [this azure and gold] at two and a half lire. 

H 125 [18 V.] r. and 124. [19 r.j V. 

428 ' , 



\Dr awing of church with section of ground plan\ 

Both lower and upper part of this edifice are usable, as in San 
Sepolcro, and it is similar in its upper and lower parts except that the 
upper part has the cupola c ^ and the lower the cupola a b. As you enter 
the lower church you descend ten steps, and when you go up into that 
above you ascend twenty steps, which reckoning each as a third of a 
braccio comes to ten braccio. This then is the distance there is between 
the level of the one church and of the other. ^ ^ 

\With architectural drawing^ 

Here a campanile neither can nor ought to be made. 

Rather must it stand separate, as it does in the cathedral, or at San 
Giovanni in Florence; and so also the cathedral at Pisa, for there the 
campanile may be seen by itself round in shape and standing apart, 
as also is the cathedral. And each by itself can reveal its perfection. 

If however anyone should desire to make it part of the church he 
should make the lantern-tower serve as a campanile, as it does in the 
church of Chiaravalle. 2037 Bib. Nat. 5 v. 

Mills should not be built by stagnant water, nor by the side of the 
sea, because the storms choke up with sand every canal that is made upon 
its shores. b.m. 63 v. 

\Foundations\ , . 

The first and most essential requisite is stability. 

As regards the foundations of the component parts of temples and 
other public buildings, their depths should bear the same relation one to 
another as do the weights which are to rest upon them. 

Each section of the depth of the earth in a given space is arranged in 
layers, the layers having each a heavier and a lighter part, the heavier 

being at the bottom. _ 1 1 j- 

This comes from the fact that these layers are formed by the sediment 
from the water discharged into the sea by the current of the rivers whic 1 

are poured into it. . , 

The heaviest part of this sediment was the part that was discharged 

first, and this process continued. , 

And this is the action of the water when it becomes stationary, and 
it is carrying it away at first where it moves. 


These layers of soil are visible in the banks of rivers which in their 
continuous course have sawn through and divided one hill from another 
in a deep defile, wherein the level of the waters has receded from the 
shingle of the banks, and this has caused the substance to become dry 
and to be changed to hard stone, especially such mud as was of the 
finest texture. And this leads us to conclude that each part of the earth’s 
surface was once the centre of the earth, and so conversely. 


A wall will always crack when it does not dry uniformly at the same 
time. ■ ■■ ' 

A wall of uniform thickness does not all become dry at the same time 
unless it is in contact with an equal medium; thus if a wall be so built that 
part of it touches a damp mound while the rest is exposed to the 
atmosphere, this latter part will become somewhat contracted while the 
damp portion will retain its original size. 

For the part which becomes dried by the atmosphere draws itself 
together and shrinks, and the part in contact with the damp does not 
become dry, and the dry part readily breaks away from the damp part 
as this has not the coherence necessary for it to follow the movement of 
the part that is in process of becoming dry. 

A N D N A R R O W B E L O W 

Those arched cracks wide above and narrow below have their origin 
in walled-up doorways, which contract more in length than in width in 
proportion as their height is greater than their breadth, and as the joins 
of the mortar are more numerous in the height than in the breadth. 

B.M. 138 r. 

When either a complete dome or a half dome is vanquished above 
by an insupportable weight, the vault will burst asunder, the crack being 
small in the upper part and broad below, and narrow on the inner side 
and wide on the outer side, after the manner of the skin of a pomegranate 
or orange which splits into many parts lengthwise, for the more it is 
pressed upon from the opposite ends, the wider asunder will those parts 

. - .Jj^'sVv* ■; 

i M 


of the joints open which are farthest away from the cause of the pressure. 
And for this reason the arches of the vaults of any apse should never be 
loaded more than the arches of the building of which it forms a part, 
especially because that which weighs most presses most heavily upon the 
parts below it and drives them down upon their foundations; but this 
cannot happen with lighter things such as the aforesaid apses. 

B.M. 141 V. 

Make first a treatise of the causes which bring about the collapse of 
walls, and then, separately, a treatise of the remedies. 

Parallel cracks are constantly appearing in buildings erected in 
mountainous places where the rocks are stratified and the stratification 
runs obliquely, for, in these oblique seams, water and other moisture often 
penetrates, bearing with it a quantity of greasy and slimy earth; and 
since this stratification does not continue down to the bottom of the 
valleys the rocks go slipping down their slope, and never end their move- 
ment until they have descended to the bottom of the valley, carrying 
with them after the manner of a boat such part of the building as they 
have severed from the rest. 

The remedy for this is to build numerous piers under the wall which 
is slipping away, with arches from one to another, and well-rooted [?] ^ 
[Pbuttressed] and let the pillars have their bases firmly set in the stratified 
rock so that they may not break away. 

In order to find the immovable part of the aforesaid stratum, it is neces- 
sary to sink a shaft through it to a great depth beneath the foot of the 
wall, and in this shaft to polish a smooth surface of the breadth of a hand 
from the top to the bottom of the side on which the hill slopes down. At 
the end of some time this smooth portion made on the side of the shaft 
will show very plainly which part of the mountain is moving. 

B.M. 157 r. 

T H E I R M O R T A R 

Stones which are built up with an equal number from bottom to top 
and laid with an equal quantity of mortar, will settle down equally as the 
moisture which softens the mortar evaporates. 

Cracks in walls will never be parallel unless the part of the wall which 
is separated from the rest does not descend. 

^ MS. abarbanati. 

■ 431 



Stability of buildings results from a law the converse of the two fore- 
going, namely that the walls should be built up all equally in equal stages, 
which should embrace the whole circuit of the building and the total 
thickness of the walls no matter of what kind; and although the thin wall 
dries more rapidly than a thick one it will not have to break as the result 
of the weight which it may acquire from one day to another; for if a 
double quantity of it were to dry in one day, a wall of double the thick- 
ness would dry in two days or thereabouts, and so a slight difference in 
weight would be balanced by a slight difference of time. 


When the crack in a wall is wider at the top than at the bottom it is 
a clear sign that the source of the destruction of the wall lies outside the 
perpendicular of the crack. bm xcyv 

P R I V A T E B U I L D I N G S 

Walls collapse as a result of cracks which are either vertical or slant- 
ing. Cracks which proceed vertically are caused by new walls being 
built in conjunction with old walls either vertically or with toothings 
fitted into the old walls; for as these toothings cannot offer any resistance 
to the insupportable weight of the wall joined on to them they must needs 
break and allow the new wall to settle down, in which process it will sink 
a braccio in every ten, or more or less according to the greater or smaller 
quantity of mortar used for the stones in the construction, and whether 
the mortar is very liquid or not. And remember always to build the walls 
first and then add the facing stones, because unless this is done, since the 
subsidence of the wall in settling will be greater than that of the outer 
shell, the toothings set in the sides of the wall will necessarily be broken, 
because the stones used for facing the walls being larger than the stones 
used in their construction will of necessity take a less quantity of mortar 
in their joints, and therefore the subsidence will be less. But this cannot 
happen if the facing of the wall is added after the wall has had time 
to dry. 

B.M. 158 r. 



\Wifh diagrams] 

Let the houses be transported and arranged in order, and this can be 
done with ease because these houses are first made in parts upon the open 
places, and are then fitted together with their timbers on the spot where 
they are to remain. 

Let fountains be made in each piazza. 

Let the countryfolk dwell in parts of the new houses when the court 
is not there. 

B.M. 270 V. 


Cover of the preaching place of the castle. 

^ ° ^ Forster 11 70 V. 

That angle will have the greatest power of resistance which is most 

acute, and the most obtuse will be the weakest. - o 

’ Forster n 87 v. 



Here it is shown how the arches made in the sides of the octagon push 
the columns of the angles outwards, as is shown in the line h c and in the 
line t d^ which push the column m outwards, that is they exert pressure 
to drive it from the centre of this octagon. Forster n 93 r 


That part of the bulk of the lower support will be more weighed 
down upon which is nearer the centre of the weight supported by it. 

Forster ni 13 v. 


That in the canals nothing be thrown, and that these canals go 
straight to the houses. Forster majv. 

The hall of the court is one hundred and twenty-eight steps long and 
its breadth is twenty-seven braccia. Forster m 49 v 


The height of the walls of the courtyard should be half its length, 
that is if the courtyard be forty braccia the house ought to be twenty 

/■■■■ ■■ , ■. 43'3 ■ 

EE 2 


high in the walls of the said courtyard, and this courtyard should be 
half the width of the whole front. Wtodson Drawings 1^585 v. 

\W ater-stair in the Sforzescd\ 

When the descent from the floodgates has been so hollowed out that 
at the end of its drop it is below the bed of the river, the waters which 
descend from them will never form a cavity at the foot of the bank, and 
will not carry away soil in their rebound, and so they will not proceed to 
form a fresh obstacle but will follow the transverse course along the length 
of the base of the floodgate from the under side. Moreover if the lowest 
part of the bank which lies diagonally across the course of the waters be 
constructed in deep broad steps after the manner of a staircase, the waters 
which as they descend in their course are accustomed to fall perpendicu- 
larly from the beginning of this lowest stage, and dig out the founda- 
tions of the bank, will not be able any longer to descend with a blow of 
irresistible force. 

And I give as an example of this the stair down which the water falls 
from the meadows of the Sforzesca at Vigevano, for the running water 
falls down it for a height of fifty braccia. ^ 

\With drawing 

Stairs of Vigevano, below the Sforzesca, with one hundred and thirty 
steps a quarter of a braccio high and half a braccio wide, down which the 
water falls without wearing away anything as it finishes its fall; and by 
these stairs so much soil has come down as to have dried up a swamp, that 
is by having filled it up; and it has formed meadows from swamps of 
great depth. _ 



‘Music which is consumed in the very act of 
its birth, (trattato i 29) 

Music has two ills, the one mortal the other wasting; the mortal is 
ever allied with the instant which follows that of the music’s utterance, 
the wasting lies in its repetition, making it seem contemptible and 
mean. „ 

C.A. 382 V. a 

\Wtth drawing 

This is the manner of movement of the bow of the viol-player; and 
if you make the notches of the wheel in two different sizes[?] {tempi), 
so that one set of teeth are less than the other and they do not meet 
together as is seen in a b, the bow will have an equal movement, other- 
wise it will go in jerks. But if you make it in the way I say the pinion jf 
will always move equally. 

B 50 V. 


Here you make a wheel with pipes that serve as clappers for a 
musical round called a Canon, which is sung in four parts, each singer 
singing the whole round. And therefore I make here a wheel with four 
cogs so that each cog may take the part of a singer. ^ ^ ^ ^ 

I have several cords drawn in octaves the one above the others, and 
I wish that each may be drawn a finger more than before. I ask what 
weight will that be which will draw it, being of equal size or of double 
size, and what sound will remain. „ 

Forster ii 35 v. 

Of the music of water falling into its vessel. 

With the help of the mill I will make unending sounds from all 
sorts of instruments, which will sound for so long as the mill shall 
continue to move. 



‘I will create a fiction which shall express great 



A certain man gave up associating with one of his friends because the 
latter had a habit of talking maliciously against all his friends. This 
friend whom he had left was once reproaching him, and after many 
complaints besought him to tell him the reason that had caused him to 
lose the recollection of so great a friendship as theirs; to which he made 
reply: I am not willing to be seen in your company any more because I 
like you, and I do not wish that by talking maliciously to others of me 
who am your friend, you may cause them to form a bad impression of 
you, as I have, through your talking maliciously to them of me who am 
your friend. Consequently as we have no more to do with each other it 
will appear that we have become enemies, and the fact that you talk of 
me maliciously, as is your habit, will not be so much worthy of rebuke as 
if we were constantly in each other’s company. ^ ^ ^ ^ 

Dear Benedetto, — To give you the news of the things here from the 
east, you must know that in the month of June there appeared a giant 
who came from the Libyan desert. This giant was born on Mount 
Atlas, and was black, and he fought against Artaxerxes with the 
Egyptians and Arabs, the Medes and Persians; he lived in the sea upon 
the whales, the great leviathans and the ships. When the savage giant 
fell by reason of the ground being covered over with blood and mire, it 
seemed as though a mountain had fallen; whereat the country [shook] 
as though there were an earthquake, with terror to Pluto in hell, and 
Mars fearing for his life fled for refuge under the side of Jove, ^ 

And from the violence of the shock he lay prostrate on the level 
ground as though stunned; until suddenly the people believing that he 
had been killed by some thunderbolt, began to turn about his great 
beard; and like a flock of ants that range about hither and thither 
furiously among the brambles beaten down by the axe of the sturdy 
peasant, so these are hurrying about over his huge limbs and piercing 
them with frequent wounds. 

At this the giant being roused and, perceiving himself to be almost 

^ MS., Marte feme do dela vita sera fugito sotto lato dj glove. These words in Leonardo’s 
writing occur at the side and are not found in the transcript of the Italian edition. I have 
ventured to insert them where they seemed to fit the sense best, and also to change the 
order of some of the sentences which are written in the margin. 

■441 . ,■ 


covered by the crowd, suddenly on feeling himself smarting from their 
stabs, uttered a roar which seemed as though it were a terrific peal of 
thunder, and set his hands on the ground and lifted up his awe-inspiring 
countenance; and then placing one of his hands upon his head, he per- 
ceived it to be covered with men sticking to the hairs after the fashion of 
tiny creatures which are sometimes harboured there, and who, as they 
clung to the hairs and strove to hide among them, were like sailors in a 
storm who mount the rigging in order to lower the sail and lessen the 
force of the wind ; and at this point he shook his head and sent the men 
flying through the air after the manner of hail when it is driven by the 
fury of the winds, and many of these men were found to be killed by 
those who fell on them like a tempest. Then he stood erect, trampling 
upon them with his feet. ^ ^ 

Note. — • This and the two pieces that follow seem parts of a fantastic tale written in 
the form of letters. 

The black visage at first sight is most horrible and terrifying to look 
upon, especially the swollen and bloodshot eyes set beneath the awful 
lowering eyebrows which cause the sky to be overcast and the earth to 

And believe me there is no man so brave but that, when the fiery 
eyes were turned upon him, he would willingly have put on wings in 
order to escape, for the face of infernal Lucifer would seem angelic by 
contrast with this. 

The nose was turned up in a snout with wide nostrils and sticking 
out of these were quantities of large bristles, beneath which was the 
arched mouth, with the thick lips, at whose extremities were hairs like 
those of cats, and the teeth were yellow; and from the top of his instep 
he towered above the heads of men on horseback. 

And as his cramped position had been irksome, and in order to rid 
himself of the importunity of the throng, his rage turned to frenzy, and 
he began to let his feet give vent to the frenzy which possessed his 
mighty limbs, and entering in among the crowd he began by his kicks 
to toss men up in the air, so that they fell down again upon the rest, as 
though there had been a thick storm of hail, and many were those who 
in dying dealt out death. And this barbarity continued until such time 
as the dust stirred up by his great feet, rising up in the air, compelled his 
infernal fury to abate, while we continued our flight. 



Alas, how many attacks were made upon this raging fiend to whom 
every onslaught was as nothing. O wretched folk, for you there avail 
not the impregnable fortresses, nor the lofty walls of your cities, nor the 
being together in great numbers, nor your houses or palaces! There 
remained not any place unless it were the tiny holes and subterranean 
caverns where after the manner of crabs and crickets and creatures like 
these you might find safety and a means of escape. Oh, how many 
wretched mothers and fathers were deprived of their children! How 
many unhappy women were deprived of their companions! In truth, my 
dear Benedetto, I do not believe that ever since the world was created 
there has been witnessed such lamentation and wailing of people, accom- 
panied by so great terror. In truth, the human species in such a plight 
has need to envy every other race of creatures; for though the eagle has 
strength sufficient to subdue the other birds, they yet remain uncon- 
quered through the rapidity of their flight, and so the swallows through 
their speed escape becoming the prey of the falcon, and the dolphins 
also by their swift flight escape becoming the prey of the whales and 
of the mighty leviathans; but for us wretched mortals there avails not 
any flight, since this monster when advancing slowly far exceeds the 
speed of the swiftest courser. 

I know not what to say or do, for everywhere I seem to find myself 
swimming with bent head within the mighty throat and remaining 
indistinguishable in death, buried within the huge belly. ^ ^ 96 v b 

\A fantasy {in Brobdingnag)’] 

He was blacker than a hornet; his eyes were as red as a burning fire 
and he rode on a big stallion six spans across and more than twenty long; 
with' six giants tied to his saddle bow and one in his hand which he 
gnawed with his teeth; and behind him came boars with tusks sticking 
out of their mouths, perhaps ten spans. 1 139 [91] r 

The gentle friar was charmed and delighted: he has already obliged 
the philosophers to search for our cause in order to feed the intellect. 

M 80 V. 

A workman who was in the habit of often going to wait upon a cer- 
tain lord without having any petition to make to him, was asked by the 
lord what his purpose was in coming; he replied that he went there to 

■ ■ '443 ' ■ . 



have one of the pleasures that he could not have, for it gave him pleasure 
to look at people who were grander than himself, as is the way with 
common folk, whereas the lord could only look at people who were of 
less account than himself, and consequently lords were cut off from this 
pleasure. Forster iii 34 v. 




‘You should often amuse yourself when you take 
a walk for recreation, in watching and taking 
note of the attitudes and actions of men as they 
talk and dispute, or laugh or come to blows one 
with another, both their actions and those of the 
bystanders who either intervene or stand looking 
on at these things/ 

A J E S T 

A priest while going the round of his parish on the Saturday before 
Easter in order to sprinkle the houses with holy water as was his custom, 
coming to the studio of a painter, and there beginning to sprinkle the 
water upon some of his pictures, the painter turning round with some 
annoyance asked him why he sprinkled his pictures in this manner. 
The priest replied that it was the custom and that it was his duty to act 
thus, that he was doing a good deed and that whoever did a good deed 
might expect a recompense as great or even greater; for so God had 
promised that for every good deed which we do on the earth we shall be 
rewarded a hundredfold from on high. Then the painter, having waited 
until the priest had made his exit, stepped to the window above and threw 
a large bucket of water down on to his back, calling out to him: — ‘See 
there is the reward that comes to you a hundredfold from on high as 
you said it would, on account of the good deed you did me with your 
holy water with which you have half ruined my pictures’. ^ ^ r 19 r a 

The Franciscan friars at certain seasons have periods of fasting, 
during which no meat is eaten in their monasteries, but if they are on a 
journey, as they are then living on almsgiving, they are allowed to eat 
whatever is set before them. Now a couple of these friars travelling 
under these conditions chanced to alight at an inn at the same time as a 
certain merchant and sat down at the same table, and on account of the 
poverty of the inn nothing was served there except one roasted cockerel. 
At this the merchant as he saw that it would be scant fare for himself 
turned to the friars and said: — ‘On days like these if I remember rightly 
you are not permitted in your monasteries to eat any kind of meat.’ The 
friars on hearing these words were constrained by their rule to admit 
without any attempt at argument that this was indeed the case: so the 
merchant had his desire and devoured the chicken, and the friars fared 
as best they could. 

Now after having dined in this wise all three table-companions set 
out on their journey together, and having gone a certain distance they 
V came to a river of considerable breadth and depth, and as they were all 

three on foot, the friars by reason of their poverty and the other from 
niggardliness, it was necessary according to the custom of the country 

. . ' ' . , ■ 447 ■ 


that one of the friars who had no shoes and stockings should carry the 
merchant on his shoulders; and consequently the friar having given him 
his clogs to hold took the man on his back. But as it so happened the 
friar when he found himself in the middle of the stream bethought him- 
self of another of his rules, and coming to a standstill after the manner of 
St. Christopher raised his head towards him who was weighing heavily 
upon him and said:— about you?’ 
‘VVhy you know quite well that I have,’ replied the other. ‘How do you 
suppose a merchant like me could travel about otherwise?’ ‘Alas!’ said 
the friar, ‘our rule forbids us to carry any money on our backs’; and he 
instantly threw him into the water. 

As the merchant was conscious that this was done as a jest and out of 
revenge for the injury he had done them he smiled pleasantly and 
pacifically, and blushing considerably from shame he endured their 

C.A, 150 V. b 

If Petrarch loved the laurel so much it was because it is good with 
sausages and thrushes; I don't attach any value to their trifles. 

Frati santi spells Pharisees. ^ 

Tr. i£ 

Tr. 63 i 


On an old man openly reviling a young one and boldly proclaiming 
that he had no fear of him, the young one made answer that his advanced 
age served him better as a protection than either his tongue or his strength. 

Tr. 71 a 


Why the Hungarians keep the double cross. 

H 62 [14] V. 

A man wishing to prove on the authority of Pythagoras that he had 
been in the world on a former occasion, and another not allowing him to 
conclude his argument, the first man said to the second:— ‘And this is a 
token that I was here on a former occasion, I remember that you were 
a miller.’ The other who felt provoked by his words agreed that it was 
true, for he also remembered as a token that the speaker had been the 
ass which had carried the flour for him. 

^ MS./<?nW. 


A painter was asked why he had made his children so ugly, when 
his figures which were dead things he had made so beautiful. His reply 
was that he made his pictures by day and his children at night. 

M 58 V. 

A sick man who was at the point of death heard someone knocking 
at the door, and on his asking one of his servants who it was who was 
knocking at the door, this servant made answer that it was someone who 
called herself Madame Bona. 

Whereat the sick man raised his arms to heaven and praised God with 
a loud voice, and then told the servants to let her in immediately in order 
that he might see a good woman before he died, because in all his life he 
had never seen one, „ , 

Forster ii 30 v. 

It was said to someone that he should rise from his bed because the 
sun had already risen; to which he made answer: — Tflhad to make as 
long a journey and to do as much as he I too should have already risen; 
but as I have such a short way to go I do not wish to get up yet awhile.’ 

Forster n 31 r. 

FF 2 




‘The mirror bears itself proudly, holding the 
queen mirrored within it, and after she has 
departed the mirror remains abject,’ 

The privet on feeling its tender branches, laden with new fruit, 
pricked by the sharp claws and beak of the troublesome blackbird, 
complained to her with pitiful reproaches, beseeching her that even if she 
plucked off her delicious fruit she would at any rate not deprive her of 
her leaves which protected her from the scorching rays of the sun, nor 
with her sharp claws rend away and strip bare her tender bark. 

But to this the blackbird replied with insolent rebuke: — ‘Silence! 
rude bramble 1 Know you not that Nature has made you to produce these 
fruits for my sustenance? Cannot you see that you came into the world 
in order to supply me with this very food? Know you not, vile thing 
that you are, that next winter you will serve as sustenance and food for 
the fire?’ To which words the tree listened patiently and not without tears. 

But a short time afterwards the blackbird was caught in a net, and 
some boughs were cut to make a cage in order to imprison her, and 
among the rest were some cut from the tender privet to serve for the 
rods of the cage; and these on perceiving that they would be the cause 
of the blackbird being deprived of liberty rejoiced and uttered these 
words: — ‘We are here, O blackbird, not yet consumed by the fire as 
you said; we shall see you in prison before you see us burnt.’ 

The laurel and the myrtle, on seeing the pear-tree being cut down, 
cried out with a loud voice:— -‘O pear-tree, where are you going? Where 
is the pride that you had when you were laden with ripe fruit? Now you 
will no longer make shade for us with your thick foliage.’ Then the 
pear-tree replied:— ‘I am going with the husbandman who is cutting 
me down and who will take me to the workshop of a good sculptor, 
who by his art will cause me to assume the form of the god Jove, and 
I shall be dedicated in a temple and worshipped by men in place of 
Jove. While you are obliged to remain always maimed and stripped of 
your branches which men shall set around me in order to do me 

The chestnut seeing a man upon the fig-tree bending its branches 
down towards himself and picking off their ripe fruit and putting it in 
his mouth, tearing it asunder and crushing it with his hard teeth, shook 
its boughs and said in a mournful whisper:— ‘O fig-tree, how much less 



favoured by Nature are you than I. Look how with me my sweet chil- 
dren all are arranged in close order, clothed first with a fine jacket over 
which is set the hard rough husk; and not content with conferring such 
benefits on me she has given them a strong dwelling, and set about it 
sharp close prickles so that the hands of man may not be able to harm 
me.’ At this the fig-tree and her children began to laugh, and when they 
had finished laughing she said .-—‘Know that man is of such a disposition 
that, as you have found, by means of rods and stones and sticks thrown 
into your branches he will deprive you of your fruit, and after it has 
fallen will crush it with his feet or with stones, in such a way that your 
offspring will issue forth from their armoured house crushed and bruised. 
But I am touched carefully by his hands and not as you are with sticks 
and stones.’ 

The idle fluttering moth, not contented with its power to fly 
wherever it pleased through the air, enthralled by the seductive flame of 
the candle, resolved to fly into it, and its joyous movement was the 
occasion of instant mourning. For in the said flame its delicate wings 
were consumed, and the wretched moth having fallen down at the foot 
of the candlestick, all burnt, after much weeping and contrition, wiped 
the tears from its streaming eyes, and lifting up its face exclaimed:— ‘O 
false light, how many are there like me who have been miserably 
deceived by you in times past! Alas! If my one desire was to behold 
the light, ought I not to have distinguished the sun from the false glimmer 
of filthy tallow.?’ 

A nut which found itself carried by a crow to the top of a lofty cam- 
panile, having there fallen into a crevice and so escaped its deadly beak, 
besought the wall by that grace which God had bestowed upon it in 
causing it to be so exalted and great, and so rich in having bells of such 
beauty and of such mellow tone, that it would deign to give it succour; 
that insomuch as it had not been able to drop beneath its old father’s 
green branches and lie in the fallow earth covered by his fallen leaves 
the wall would not abandon it, for when it found itself in the fierce 
crow’s cruel beak it had vowed that if it escaped thence it would end its 
days in a small hole. At these words the wall, moved with compassion, 
was content to give it shelter in the spot where it had fallen. And within 
a short space of time the nut began to burst open and to put its roots in 


among the crevices of the stones, and push them farther apart and throw 
up shoots out of its hollow, and these soon rose above the top of the 
building; and as the twisted roots grew thicker they commenced to tear 
asunder the walls and force the ancient stones out of their old positions. 
Then the wall too late and in vain deplored the cause of its destruction, 
and in a short time it was torn asunder and a great part fell in ruin. 

The ape on finding a nest of small birds approached them with great 
joy, but as they were already able to fly he could only catch the smallest. 
Filled with joy he went with it in his hand to his hiding place; and having 
commenced to look at the tiny bird he began to kiss it; and in his un- 
controllable affection he gave it so many kisses and turned it over and 
squeezed it, until he took away its life. This is said for those who by 
being too fond oT their children bring misfortune upon them, 6 t t & 

The unhappy willow, on finding herself unable to enjoy the pleasure 
of seeing her slender boughs attain to such a height as she desired, or 
even point towards the sky, because she was continually being maimed 
and lopped and spoiled for the sake of the vine or any other tree which 
happened to be near, summoned up all her faculties and by this means 
opened wide the portals of her imagination, remaining in continual 
meditation, and seeking in the world of plants for one wherewith to ally 
herself which could not need the help of her branches. So continuing 
for a time with her imagination at work, the thought of the gourd 
suddenly presented itself to her mind, and all her branches quivered in 
her intense joy, for it seemed to her that she had found the right com- 
panion for the purpose she desired, because the gourd is by nature more 
fitted to bind others than to be bound herself. After coming to this con- 
clusion she lifted up her branches towards the sky and waited, on the 
look out for some friendly bird to serve as the intermediary of her 
desire. Among the rest she descried the magpie near to her and said to 
him:-~‘0 gentle bird, by the refuge you have lately found among my 
branches at dawn, when the hungry, cruel, and rapacious falcon has 
wished to devour you, — by that rest you have often found in me when 
your wings craved rest, — by those delights you have enjoyed among my 
branches in amorous dalliance with your companions, ■— I entreat you 
to go and seek out the gourd and obtain from her some of her seeds, 
^ per non gastigare, 

■ ■ ■ . ,455 


telling her that I will care for whatever is born from them as though they 
were my own offspring, and in like manner use all such words as may 
incline her to the like purpose, though to you who are a master of 
language there is no need for me to give instruction. If you will do this 
I am content to let your nest be in the fork of my boughs together with 
all your family without payment of any rent.’ So the magpie, after 
stipulating with the willow for certain further conditions, the most im- 
portant being that she should never admit upon her boughs any snake 
or polecat, cocked his tail and lowered his head, and casting himself 
loose from the bough let himself float on his wings; and beating about 
with these in the fleeting air, seeking hither and thither, and guiding 
himself by using his tail as a rudder, he came to a gourd, and after 
courteously saluting her obtained by a few polite words the seeds for 
which he sought. On taking these back to the willow he was welcomed 
with joyful looks; and then scraping away with his foot some of the 
earth near the willow he planted the grains with his beak round about 
her in a circle. 

These soon began to grow, and as the branches increased and opened 
out they began to cover all the branches of the willow, and their great 
leaves shut away from it the beauty of the sun and the sky. And all this 
evil not sufficing, the gourds next began to drag down to the ground in 
their rude grip the tops of the slender boughs, twisting them and distort- 
ing them in strange shapes. Then the willow after shaking and tossing 
herself to no purpose to make the gourds loose their hold, and vainly for 
days cherishing such idle hopes, since the grasp of the gourds was so sure 
and firm as to forbid such thoughts, seeing the wind pass by, forthwith 
commended herself to it. And the wind blew hard; and it rent open the 
willow’s old and hollow trunk, tearing it in two parts right down to its 
roots; and as they fell asunder she vainly bewailed her fate, confessing 
herself born to no good end. 

Some flames had already lived for a month in a glass-furnace when 
they saw a candle approaching in a beautiful and glittering candlestick. 
They strove with great longing to reach it; and one of their number left 
its natural course and wound itself into an unburnt brand upon which it 
fed, and then passed out at the other end by a small cleft to the candle 
which was near, and flung itself upon it, and devouring it with the utmost 
voracity and greed consumed it almost entirely; then desirous of pro- 

456. ' 


longing its own life, it strove in vain to return to the furnace which it had 
left, but was forced to droop and die together with the candle. So at last 
in lamentation and regret it was changed to foul smoke, leaving all its 
sisters in glowing and abiding life and beauty. 

Wine, the divine liquor of the grape, finding itself in a golden richly 
chased cup upon Mahomet’s table, after being transported with pride at 
such an honour, was suddenly assailed by a contrary feeling, and said 
to itself:— What am I doing? What is it that I am rejoicing at? Cannot I 
see that I am near to my death, in that I am about to leave my golden 
dwelling in this cup and enter into the foul and fetid caverns of the 
human body, to be there transformed from a sweet fragrant nectar to a 
foul and disgusting fluid? And such an evil not sufficing, I must needs 
lie for a long time in foul receptacles with other noisome and putrid 
matter evacuated from the human intestines.’ It cried to heaven demand- 
ing vengeance for such injury and that an end might be put to such an 
insult, so that since that part of the country produced the most beautiful 
and finest grapes in the whole world these at least should not be turned 
into wine. Then Jove caused the wine which Mahomet drank to rise in 
spirit up to the brain, and to infect this to such a degree as to make him 
mad; and he committed so many follies that when he came to his senses 
he made a decree that no Asiatic should drink wine; and thus the vine 
and its fruits were left at liberty. 

As soon as the wine has entered into the stomach it commences to 
swell up and boil over; and then the spirit of that man commences to 
abandon his body, and rising as though towards the sky it reaches the 
brain, which causes it to become divided from the body; and so it begins 
to infect him and to cause him to rave like a madman; and so he per- 
petrates irreparable crimes, killing his own friends. 

c.A. 67 r. b 

The rat was being besieged in its tiny house by the weasel which 
with unceasing vigilance was awaiting its destruction, and through a tiny 
chink it was considering its great danger. Meanwhile the cat came and 
suddenly seized hold of the weasel and immediately devoured it. There- 
upon the rat, profoundly grateful to its deity, having offered up some of 
its hazel-nuts as a sacrifice to Jove, issued forth from its hole in order to 
repossess itself of the liberty it had lost, and was instantly deprived of 
this and of life itself by the cruel claws and teeth of the cat. 


C.A. 67 V. a 


Fable of the tongue bitten, by the teeth. 

The cedar, arrogant by reason of its beauty, despising the plants which 
were round about it, caused them to be all removed from its presence, 
and then the wind, not meeting with any obstacle, tore it up by the roots 
and threw it on to the ground. 

The ant having found a grain of millet, the grain as it felt itself 
seized by it cried out:— Tf you will do me the great favour of allowing me 
to fulfil my desire to germinate I will give you of myself a hundredfold.’ 
And so it was. 

The spider, having found a bunch of grapes, which because of its 
sweetness was much visited by bees and various sorts of flies, fancied that 
it had found a spot very suitable for its wiles. And after having lowered 
itself down by its fine thread and entered its new habitation, there day by 
day, having ensconced itself in the tiny holes made by the spaces between 
the various grapes in the bunch, like a robber it assaulted the wretched 
animals which were not on their guard against it. But after some days 
had passed the keeper of the vineyard cut this bunch off and placed it 
with the others, and it was pressed with them. And the grapes therefore 
served as trap and snare for the deceiving spider as well as for the flies 
whom he had deceived. 

The traveller’s joy, not remaining contented in its hedge, commenced 
to pass across the high road with its branches and to attach itself to the 
opposite hedge; whereupon it was broken by the passers-by. 

The ass having fallen asleep upon the ice of a deep lake, the heat of 
its body caused the ice to melt, and the ass being under water awoke to 
his great discomfort, and was speedily drowned. 

A certain patch of snow, finding itself clinging to the top of a rock 
which was perched on the extreme summit of a very high mountain, 
being left to its own imagination began to reflect and to say within itself: 
— ‘Shall I not be thought haughty and proud for having placed myself 
in so exalted a spot, being indeed a mere morsel of snow.? And for allow- 
ing that such a vast quantity of snow as I see around me should take a 
lower place than mine.? Truly my small dimensions do not deserve this 
■■ 458 


eminence; and in proof of my insignificance I may readily acquaint 
myself with the fate which but yesterday befell my companions, who in 
a few hours were destroyed by the sun; and this came about from their 
having placed themselves in a loftier station than was required of them. 
I will flee from the wrath of the sun, and abase myself, and find a place 
that befits my modest size.’ 

Then throwing itself down, it began to descend, rolling down from 
the lofty crags on to the other snow; and the more it sought a lowly 
place, the more it increased in bulk, until at last ending its course upon a 
hill, it found itself almost the equal in size of the hill on which it rested, 
and it was the last of the snow which was melted that summer by the 

This is said for those who by humbling themselves are exalted. 

The hawk, being unable to endure with patience the way in which the 
duck was hidden from him when she fled before him and dived beneath 
the water, desired also to follow in pursuit beneath the water; and getting 
its wings wetted it remained in the water; and the duck raised herself 
in the air and mocked at the hawk as it drowned. 

The spider, wishing to capture the fly in its secret web, was cruelly 
slain above it by the hornet. 

The eagle, wishing to mock at the owl, got its wings smeared with 
bird-lime and was captured by man and killed. ^ ^ ^ ^ 


The cedar, having conceived the desire of bearing on its summit a 
large and beautiful fruit, set itself to carry it into effect with all the 
powers of its sap; which fruit after it had grown was the cause of making 
the tall and slender summit bend down. 


The peach-tree, being envious of the great quantity of fruit that it 
saw its neighbour the nut-tree bearing, decided to do the same, and loaded 
itself with its fruit to such an extent that the weight of this fruit threw it 
down, uprooted and broken, level with the ground. 




The nut-tree, displaying to the passers-by upon the road the richness 
of its fruit, every man stoned it. 

When the fig-tree stood without fruit no one looked at it. Wishing 
by producing this fruit to be praised by men, it was bent and broken by 

The fig-tree, standing near to the elm, and perceiving that her boughs 
bore no fruit themselves, yet had the hardihood to keep away the sun 
from her own, unripe figs, rebuked her, saying:— 'O Elm, are you not 
ashamed to stand in front of me? Only wait until my children are fully 
grown and you will see where you will find yourself.’ But when her off- 
spring were ripe a regiment of soldiers came to the place, and they tore 
off the branches of the fig-tree in order to take her figs, and left her all 
stripped and broken. 

And as she thus stood maimed in all her limbs the elm questioned her 
saying:— ‘O Fig tree, how much better was it to be without children than 
to be brought by them to so wretched a pass?’ c a 76 r a 

The fire rejoicing in the dried wood which it had found in the fire- 
place, and having taken hold of it, perceiving itself to have grown 
enormously above the wood and to have made itself of considerable size, 
commenced to exalt its gentle and tranquil soul in puffed -up and insup- 
portable pride, making itself almost believe that it had drawn the whole 
of the superior element down into the few logs. And commencing to 
fume and fill all the fireplace round about it with explosions and showers 
of sparks, already the flames which had become big were all in conjunc- 
tion making their way towards the air; then the highest flames striking 
upon the bottom of the saucepan above ... 

A vestige of fire which had remained in a small lump of charcoal 
among the warm embers, was very scantily and poorly nourished by 
the small quantity of nutriment that was left there. When the superin- 
tendent of the kitchen arrived there in order to perform her usual work 
of preparing the food, having placed the logs on the hearth, and having 
succeeded by means of a sulphur-match in getting a small flame from 
the charcoal though it was almost extinct, she set it among the logs 



which she had arranged and took a saucepan and set it over it and 
without any misgivings went away from it. 

Then the fire, after rejoicing at the dried logs placed upon it, began 
to ascend and drive out the air from the spaces between the logs, twining 
itself in among them in sportive and joyous progress, and having com- 
menced to blow through the spaces between the logs out of which it had 
made delightful windows for itself, and to emit gleaming and shining 
flames, it suddenly dispels the murky darkness of the closed-in kitchen, 
and the flames having already increased began to play joyfully with the 
air that surrounded them, and singing with gentle murmur they created 
a sweet sound. . , 

C.A. I 10 V, D 

The thrushes rejoiced greatly on seeing a man catch the owl and 
take away her liberty by binding her feet with strong bonds. But then 
by means of bird-lime the owl was the cause of the thrushes losing not 
only their liberty but even their life. This is said of those states which 
rejoice at seeing their rulers lose their liberty, in consequence of which 
they afterwards lose hope of succour and remain bound in the power of 
their enemy, losing their liberty and often life. ^ ^ 

While the dog was asleep on the coat of a sheep, one of its fleas, be- 
coming aware of the smell of the greasy wool, decided that this must be 
a place where the living was better and more safe from the teeth and 
nails of the dog than getting his food on the dog as he did. Without 
more reflection therefore it left the dog and entering into the thick wool 
began with great toil to try to pass to the roots of the hairs; which enter- 
prise however after much sweat it found to be impossible, owing to these 
hairs being so thick as almost to touch each other, and there being no 
space there where the flea could taste the skin. Consequently after long 
labour and fatigue it began to wish to go back to its dog which however 
had already departed, so that after long repentance and bitter tears it 
was obliged to die of hunger. 

° ° C.A. 1191. a 

Once upon time the razor emerging from the handle which served 
it as a sheath, and placing itself in the sun, saw the sun reflected on its 
surface, at which thing it took great pride, and turning it over in its 
thoughts it began to say to itself:— ‘Am I to go back any more tojthat shop 
from which I have just now come away? No surely! It cannot be the 



pleasure of the gods that such radiant beauty should stoop to such vile 
uses ! What madness would that be which should induce me to scrape the 
lathered chins of rustic peasants and to do such menial service? Is this 
body made for actions such as these? Certainly notl I will go and hide 
myself in some retired spot, and there pass my life in tranquil ease.’ 

And so having hidden itself away for some months, returning one 
day to the light and coming out of its sheath it perceived that it had 
acquired the appearance of a rusty saw, and that its surface no longer 
reflected the sun’s radiance. In vain with useless repentance it bemoaned 
its irreparable hurt, saying to itself:— ‘Ah how much better would it have 
been to have let the barber use that lost edge of mine that had so rare a 
keenness! Where now is the glittering surface? In truth the foul in- 
sidious rust has consumed it away 1’ 

The same thing happens with minds which in lieu of exercise give 
themselves up to sloth; for these like the razor lose their keen edge, and 
the rust of ignorance destroys their form. 

A stone of considerable size, only recently left uncovered by the 
waters, stood in a certain spot perched up at the edge of a delightful 
copse, above a stony road, surrounded by plants bright with various 
flowers of different colours, and looked upon the great mass of stones 
which lay heaped together in the road beneath. And she became filled 
with longing to let herself down there, saying within herself:— ‘What am 
I doing here with these plants? I would fain dwell in the company of 
my sisters yonder’ ; and so letting herself fall she ended her rapid course 
among her desired companions. But when she had been there for a 
short time she found herself in continual distress from the wheels of 
the carts, the iron hoofs of the horses and the feet of the passers-by. 
One rolled her over, another trampled upon her; and at times she raised 
herself up a little as she lay covered with mud or the dung of some animal, 
and vainly looked up at the place from whence she had departed as a 
place of solitude and quiet peace. 

So it happens to those who, leaving a life of solitude and contempla- 
tion, choose to come and dwell in cities among people full of infinite 


As the painted butterfly was idly wandering and flitting about 
through the darkened air a light came within sight, and thither 




immediately it directed its course, and flew round about it in varying 
circles marvelling greatly at such radiant beauty. And not contented 
merely to behold, it began to treat it as was its custom with the fragrant 
flowers, and directing its flight it approached with bold resolve close to 
the light, which thereupon consumed the tips of its wings and legs and 
the other extremities; and then dropping down at the foot of it, it began 
to consider with astonishment how dbis accident had been brought about; 
for it could not so much as entertain a thought that any evil or hurt could 
possibly come to it from a thing so beautiful; and then having in part 
regained the strength which it had lost, it took another flight and passed 
right through the body of the flame, and in an instant fell down burned 
into the oil which fed the flame, preserving only so much life as sufficed 
it to reflect upon the cause of its destruction, saying to it:— ‘O accursed 
light! I thought that in you I had found my happiness! Vainly do I 
lament my mad desire, and by my ruin I have come to know your 
rapacious and destructive nature.’ 

To which the light replied:— ‘Thus do I treat whoever does not 
know how to use me aright.’ 

This is said for those who when they see before them these carnal and 
worldly delights, hasten towards them like the butterfly, without ever 
taking thought as to their nature, which they know after long usage to 
their shame and loss. 

The flint on being struck by the steel marvelled greatly and said to 
it in a stern voice:— ‘What arrogance prompts you to annoy me? Trouble 
me not, for you have chosen me by mistake; I have never done harm to 
anyone.’ To which the steel made answer:— ‘If you will be patient you 
will see what a marvellous result will issue forth from you.’ 

At these words the flint was pacified and patiently endured its martyr- 
dom, and it saw itself give birth to the marvellous element of fire which 
by its potency became a factor in innumerable things. 

This is said for those who are dismayed at the outset of their studies, 
and then set out to gain the mastery over themselves and in patience to 
apply themselves continuously to those studies, from which one sees result 
things marvellous to relate. , 

® C.A. 257 r. b 

The lily planted itself down upon the bank of the Ticino, and the 
stream carried away the bank and with it the lily. ^ ^ 


The oyster being thrown out with other fish near to the sea from the 
house of a fisherman, prayed to a rat to take him to the sea; the rat who 
was intending to devour him bade him open, but then as he bit him the 
oyster squeezed his head and held it; and the cat came and killed him. 


The pen has necessary companionship with the penknife, and more- 
over useful companionship for the one without the other is ineffective. 

L cover V. 

When the crab had placed itself beneath the rock in order to catch 
the fish that entered underneath it, the wind came with ruinous downfall 
of the rocks, and these by rolling themselves down destroyed the crab. 

The spider had placed itself among the grapes to catch the flies that 
fed on them. The time of vintage came and the spider was trodden 
under foot together with the grapes. 

The vine that has grown old upon the old tree falls together with the 
destruction of this tree. It was by reason of its bad company that it 
failed together with it. 

The torrent carried away so much earth and stones in its bed that it 
was then obliged to change its position. 

The net which was accustomed to catch fish was destroyed and 
carried away by the fury of the fish. 

The ball of snow the more it rolled as it descended from the moun- 
tains of the snow was continually more and more increasing its size. 

The willow which by reason of its long shoots and by growing so as 
to surpass every other plant had become the companion of the vine 
which is pruned every year, was also itself always mutilated. ^ ^2 v 

The water on finding itself in the proud sea, its element, was seized 
with a desire to rise above the air; and aided by the element of fire 
having mounted up in thin vapour, it seemed almost as thin as the air 
itself; and after it had risen to a great height it came to where the air 
was more rarefied and colder, and there it was abandoned by the fire; 



and the small particles being pressed together were united and became 
heavy; and dropping from thence its pride was put to rout, and it fell 
from the sky, and was then drunk up by the parched earth, where for a 
long time it lay imprisoned and did penance for its sin. 

^ rorster ni 2 r. 

The light above the candle is fire in a chain; consuming that it con- 
sumes itself. 

The wine consumed by the drunkard, this wine revenges itself upon 
the drinker. 

rorster iii 21 r. 

The ink is arraigned for its blackness by the whiteness of the paper, 
which sees itself soiled by it. 

The paper on seeing itself all spotted by the murky blackness of the 
ink grieves over it; and this ink shows it that by the words which it com- 
poses upon it it becomes the cause of its preservation. -r. , 

^ r r rorster iii 27 r. 

The fire, when heating the water placed in the cooking-pot, says 
to the water that it does not deserve to stand above the fire, the king of 
the elements; and so it wishes by the violence with which it boils to 
drive away the water from the cooking-pot; this, therefore, in order to 
show it honour by obeying it, descends below and drowns the fire. 

Forster III 30 r. 

The knife, an artificial weapon, deprives man of his nails — his 
natural weapon. 

The mirror bears itself proudly, holding the queen mirrored within 
it, and after she has departed the mirror remains abject. 

Forster m 44 v. 

The heavy iron is reduced to such a state of thinness by the file that 
a breath of wind suffices to carry it away. 

J J Forster in 47 r. 

The plant complains of the dry and old stick which was placed at its 
side and of the dry stakes that surround it; the one keeps it upright, the 
other protects it from bad companions. 

^ ^ Forster in 47 v. 

GG 2 




A Bestiary 

‘Nature has given such power of understanding 
to animals that in addition to the perception of 
what is to their own advantage they know 
what is to the disadvantage of the enemy.’ 


The lark is a bird of which it is told that if it is taken into the presence 
of anyone who is ill, then if the sick person is going to die the bird turns 
away its head and does not look at him. But if the sick person is going 
to recover, the bird never takes its eyes off him, and is the cause of all his 
sickness leaving him. Similarly the love of virtue never regards a mean 
or bad thing, but always rather dwells among things honest and virtuous, 
and repatriates itself in noble hearts like birds in green forests upon 
flowery branches. And this love reveals itself more in adversity than in 
prosperity, acting as does light which shines most where it finds the 
darkest spot. ^ ^ ^ ^ 


Of the kite one reads that when it sees that its children in the nest are 
too fat it pecks their sides out of envy and keeps them without food. 


Cheerfulness is characteristic of the cock, for it rejoices over every 
little thing and sings with varied and joyous movements. 


Sadness may be compared to the raven, which on seeing its newborn 
children white, departs with great grief and abandons them with sad 
lamentations, and does not give them any food until it discerns a few 
black feathers. ^ ^ ^ 


Of the beaver one reads that when it is pursued, knowing this to be 
on account of the virtue of its testicles for medicinal uses, not being able 
to flee any farther it stops, and in order to be at peace with its pursuers 
j bites off its testicles with its sharp teeth and leaves them to its enemies. 

1 The allegories about animals in this Manuscript are derived from early bestiaries. 
The extent of Leonardo’s debt to his sources is set forth by Gerolamo Calvi in II 
Manoscrifto H di L da V. 11 ‘■Fiore di Virtu' e VAcerba di Cecco d'Ascoli. Archivio 
Storico Lombardo Anno XXV Fasc. XIX 1898. 

i'... . #9 ■. .... ' 



It is said of the bear that when he goes to the beehives to take the 
honey from them, the bees commence to sting him, so that he leaves the 
honey and rushes to avenge himself; and wishing to take vengeance upon 
all those who are biting him he fails to take vengeance on any, with 
result that his course becomes changed to frenzy, and in his exasperation 
he throws himself upon the ground, vainly trying to defend himself with 
his hands and feet. . 

H 6 r, 


The virtue of gratitude is said to be found especially in the birds 
called hoopoes, which being conscious of the benefits they have received 
from father and mother in life and nourishment, when they see these 
becoming old Make a nest for them and cherish them and feed them, 
plucking out their old and shabby feathers with their beaks, and by 
means of certain herbs restoring their sight, so that they return to a state 
of prosperity. 


The toad feeds on earth and always remains lean because it never 
satisfies itself, so great is its fear lest the supply of earth should fail. 

H 6 V. 


The pigeons serve as a symbol of ingratitude; for when they are of 
an age no longer to have need of being fed, they commence to fight with 
their father, and the combat does not end until the young one has driven 
his father out and taken his wife and made her his own. 


The basilisk is so exceedingly cruel that when it cannot kill animals 
vith the venom of its gaze it turns towards the herbs and plants, and look- 
ing fixedly upon them makes them wither up. ^ ^ p 

M A G N A N I M I T Y 

Of the eagle it is said that it never has so great a hunger that it does 
not leave of its prey to those birds which are round about; and as these 
are not able to forage for themselves it is necessary that they pay court 
to the eagle, since by this means they are fed. 



If the wolf while prowling warily round some cattle-stall should 
chance to set his foot in a trap so that he makes a noise, he bites his foot 
off in order to punish himself for his mistake. ^ ^ 


The siren sings so sweetly as to lull the mariners to sleep, and then 
she climbs upon the ships and kills the sleeping mariners. 


The ant from its natural sagacity provides in the summer for the 
winter, killing the seeds after having gathered them, in order that they 
may not germinate, and then in time it eats them. 


As the wild bull hates the colour red the hunters drape in red the 
trunk of a tree, and the bull charges it furiously and gets his horns fixed 
in it, and then the huntsmen kill him. ^ g ^ 


We may compare the virtue of justice to the king of the bees, who 
orders and arranges everything on a system, because some bees are 
ordered to go among the flowers, others are ordered to work, others to 
fight with the wasps, others to take away the dirt, others to accompany 
and attend the king. And when he becomes old and has no wings they 
carry him, and if any one of them fail in his duty he is punished without 
any forgiveness. 


Although partridges steal each other’s eggs nevertheless the children 
born from these eggs always return to their true mother. ^ g ^ 


The cranes are so faithful and loyal to their king that at night when 
he is asleep some pace up and down the meadow to keep guard over him 
from a distance; others stand near at hand, and each holds a stone in his 
foot, so that if sleep should overcome them the stone would fall and make 
such a noise that they would be wakened up. There are others who sleep 





together around the king, and they do this every night taking it in turn 
so that their king may not come to find them wanting. 


The fox when he sees a flock of magpies or jackdaws or birds of this 
kind, instantly throws himself on the ground with mouth open in such a 
way as to seem dead: the birds think to peck at his tongue and he bites 
off their heads. 

H 9 r. 


The mole has very small eyes and always remains underground; it 
lives as long as it stays in concealment, and as soon as ever it comes to the 
light it instantly dies, because it becomes known — So it is with a lie. 


The lion never feels fear; on the contrary it fights with a stout heart 
in fierce combat against the crowd of hunters, always seeking to injure 
the first who has injured him. 


The hare is always timid, and the leaves that fall from the trees in 
autumn keep it always in fear and often cause it to flee. 

i J H 9 V. 


The falcon only preys on large birds, and it would let itself die before 
it would feed on the young or eat putrid flesh. 


As regards this vice we read of the peacock being more subject to it 
than any other creature, because it is always contemplating the beauty 
of its tail, spreading it out in the form of a wheel and attracting to itself 
by its cries the attention of the surrounding animals. 

And this is the last vice that can be conquered. 

^ H lo r. 


For constancy the phoenix serves as a type; for understanding by 
nature its renewal it is steadfast to endure the burning flames which con- 
sume it, and then it is reborn anew. 

British Museum 
[Text : n. 473I 




The swift is put for inconstancy, for it is always in movement, since it 
cannot endure the slightest discomfort. 


The camel is the most lustful animal that there is, and it will follow 
the female a thousand miles, but if it lived continually with its mother 
or sister it would never touch them, so well does it know how to control 


The unicorn through its lack of temperance, and because it does not 
know how to control itself for the delight that it has for young maidens, 
forgets its ferocity and wildness; and laying aside all fear it goes up to the 
seated maiden and goes to sleep in her lap, and in this way the hunters 
take it. 


Of humility one sees the supreme instance in the lamb, which sub- 
mits itself to every animal. And when they are given as food to lions in 
captivity they submit themselves to them as to their own mothers, in 
such a way that it has often been seen that the lions are unwilling to kill 

The falcon from its haughtiness and pride thinks to overcome and 
lord it over all the other birds of prey, because it wishes to reign alone: 
and many times the falcon has been seen to attack the eagle the queen of 


The wild ass if when going to the spring to drink it should find the 
water muddy, has never so great a thirst as to cause it not to abstain from 
drinking and wait until the water grows clear. 


The vulture is so given up to gluttony that it would go a thousand 
miles in order to feed on carrion, and this is why it follows armies. 




The turtle-dove never wrongs its mate; and if the one dies the other 
observes perpetual chastity, and never rests upon a green branch or drinks 
of clear water. 


The bat by reason of its unbridled lewdness does not follow any 
natural law in pairing, but male goes with male, female with female, 
as they chance to find themselves together. 


The ermine because of its moderation eats only once a day, and it 
allows itself to be captured by the hunters rather than take refuge in a 
muddy lair, in order not to stain its purity. 


The eagle when it is old flies so high that it scorches its feathers; 
and nature consents that it renews its youth by falling into shallow 

And if its young ones cannot bear to gaze at the sun it does not feed 
them. No bird that does not wish to die should approach its nest. The 
animals go much in fear of it but it does not harm them. It always leaves 
them a portion of its prey. 


This is born in Asia Magna and shines so brightly that it absorbs its 
shadows. And in dying it does not lose this light, and the feathers never 
fall out. And the feather which is detached ceases to shine. 

H 12 V. 


This bears a great love to its young; and if it finds them slain in the 
nest by a serpent it pierces itself to the heart in their presence, and by 
bathing them with a shower of blood it restores them' to life. 


The salamander in the fire refines its rough skin. — For virtue. 

It has no digestive organs and does not seek any other nourishment 
than fire, and often in tliis it renews its rough skin. 




This lives on air and it is there at the mercy of all the birds. And in 
order to be safer it flies above the clouds, and there finds an air that is so 
rarefied as to be incapable of supporting any bird that would follow it. 

At this height there flies nothing save that to whom it is given by the 
heavens: it is there that the chameleon flies. 

H 13 r, 


The alepo cannot live out of water. 


For armies, food of commanders. 

It extracts nourishment from iron; hatches eggs by its gaze. 


The swan is white without any spot, and sings sweetly as it dies; this 
song ends its life. 


It cures itself of sickness by drinking salt water. If it finds its com- 
panion in fault it abandons her. When it is old its young ones brood over 
it and nourish it until it dies. 

H 13 V. 


This with its song puts the cuckoo to silence. It dies in oil and' is 
revived in vinegar. It sings through the burning heats. 


For vice which cannot endure where virtue is. 

This loses its sight more where the light has more radiance, and be- 
comes more blinded the more it looks at the sun. 

P A R T R I D G E 

This changes from female to male and forgets its former sex. Out 
of envy it steals the eggs of others and hatches them, but the young ones 
follow their true mother. 




This by means of celandine opens the eyes of its little ones when 


This opens completely when the moon is full: and when the crab 
sees it it throws a piece of stone or a twig into it and thus prevents it 
from closing up, so that it serves the crab for a meal. 

So it may be with the mouth when it tells its secret, that it puts itself 
at the mercy of the indiscreet listener. 


This is shunned by all the serpents; the weasel fights with it by means 
of rue and slays it. Rue for virtue. 

This carries sudden death in its fangs; and in order not to hear the 
enchantments it stops up its ears with its tail. h 14 v 


This twines itself round the legs of the elephant, and it falls upon 
him and both die. And in dying it has its revenge. 

This in pairing buries her mouth and at the end clenches her teeth 
and kills her husband; afterwards the sons having waxed big within her 
body tear open her belly and slay their mother. 


The saliva spat out upon the scorpion when fasting slays it after the 
manner of abstinence from gluttony, which carries away and puts an 
end to the illnesses that proceed from this gluttony, and opens the path 
to the virtues. 

H 15 r. 


This animal seizes a man and instantly kills him; and after he is dead 
it mourns for him with a piteous voice and many tears, and having 
ended its lament it cruelly devours him. It is thus with the hypocrite, 




whose face is bathed with tears over every slight thing, showing himself 
thus to have the heart of a tiger; he rejoices in his heart over another’s 
misfortunes with a face bedewed with tears. 


The toad shuns the light of the sun: if however it be kept in it by 
force it puffs itself out so much as to hide its head below and deprives 
itself of its rays. So acts whoever is the enemy of clear and radiant virtue, 
who cannot maintain itself in its presence save by force, with puffed-up 

° H 17 r. 


The caterpillar which through the care exercised in weaving round 
itself its new habitation with admirable design and ingenious workman- 
ship, afterwards emerges from it with beautiful painted wings, rising on 
these towards heaven. 


The spider brings forth out of herself the delicate and subtle web 
which gives back to it as its reward the prey that it has taken. 

H 17 V. 


This animal with its resounding roar rouses its cubs on the third day 
after their birth and teaches them the use of all their dormant senses, 
and all the wild creatures which are in the forest flee away. 

One may liken these to the children of virtue who are wakened by 
the sound of praise: their studies grow in distinction, raising them 
continually more and more, and at the sound all that is evil flees away, 
shunning those who are virtuous. . 

The lion also covers over his tracks so as to leave nothing to indicate 
his course to his enemies. So it is well for captains that they should 
conceal the secrets of their minds, in order that the enemy may have no 
conception of their plans. ^ ^ ^ ^ 


The bite of the tarantula fixes a man in his purpose, that is in what he 
was thinking about when he was bitten. 




These punish those who have a skirmish with them by depriving 
them of life; and nature has so ordained in order that they may be fed. 

H l8 V. 


The great elephant has by nature qualities which rarely occur 
among men, namely probity, prudence, and the sense of justice and of 
religious observance. Consequently when there is a new moon they 
go to the rivers, and there having solemnly purified themselves they 
proceed to bathe, and after thus saluting the planet they go back to the 
woods. And when they are ill they throw themselves upon their backs 
and toss up plants towards heaven as though they wished to offer 
sacrifice. They bury their tusks when they drop out from old age. Of 
these two tusks they use one to dig up roots in order to feed themselves 
and keep the point of the other sharp in order to fight with it. 

When they are conquered by the hunters and overcome by fatigue 
the elephants clash their tusks, and having thus broken them off use them 
for their ransom. 

They are mild in disposition and are conscious of dangers. 

If one of them should come upon a man alone who has lost his way 
he puts him back peacefully in the path from which he has wandered. 
If he should come upon the man’s footprints before he sees him he fears 
a snare, and so he stops and blows through his trunk as he shows them to 
the other elephants; and these then form themselves into a company 
and advance cautiously. 

These animals always proceed in companies. The oldest goes in 
front and the next oldest remains the last, and thus they enclose the 

They fear shame and only pair at night and secretly, and do not 
rejoin the herd after pairing until they have first bathed themselves in 
the river. 

They do not fight over their females as other creatures do. 

It is so peaceable that its nature does not allow it willingly to injure 
creatures less powerful than itself. If it should chance to meet a drove or 
flock of sheep it puts them aside with its trunk so as to avoid trampling 
upon them with its feet; and it never injures others unless it is provoked. 
\^en one of them has fallen into a pit the others fill the pit with branches, 



earth and stones, so that they raise the floor in such a way that it may 
easily make its escape. They have a great dread of the grunting of pigs 
and retreat hastily before it, causing no less damage with their feet to 
each other than to their enemies. They delight in rivers and are always 
wandering about in their vicinity; but on account of their great weight 
they are unable to swim. They devour stones, and the trunks of trees 
are their most welcome food. They hate rats. Flies are much attracted 
by their smell, and as they settle on their backs they wrinkle up their 
skin, deepening its tight folds, and so kill them. 

When they are crossing rivers they send their young towards the 
fall of the stream, and standing themselves up stream they break the 
united course of the water so that the current may not carry them away. 

The dragon throws itself under the elephant’s body, twines its tail 
round its legs and clings to its ribs with wings and claws and bites open 
its throat. The elephant falls on top of it and the dragon bursts open; 
thus it revenges itself by the death of its enemy. 

H 19 r. and v., 20 r. and v. 

T H E D R A G O N 

These band themselves together in companies and twine after the 
manner of roots, cross swamps with their heads raised and swim towards 
where they find better pasture; and if they did not thus combine they 
would be drowned. — So the union is made. , 

H 20 V. and 21 r. 


The serpent, a very large animal, when it sees a bird in the air 
inhales its breath with such vigour as to draw the birds into its mouth. 
Marcus Regulus the Consul of the Roman army was with his army 
attacked by such a monster and almost routed. After the creature had 
been slain by a catapult it was found to measure a hundred and twenty- 
five feet, that is sixty-four and a half braccia:^ its head towered above all 
the trees in a wood. 

H 21 r. 


This is a great snake which twines itself round the legs of the cow 
in such a way that it cannot move, and then it sucks it so as almost to 
^ It is not always possible to harmonize Leonardo’s measurements. 



dry it up. One of the species was killed on the hill of the Vatican in the 
time of the Emperor Claudius, and it had a whole boy inside it whom it 
had swallowed. 

H 21 r. and v. 


This beast is a native of the island of Scandinavia. It has the shape 
of a great horse except for the differences caused by the great length of 
the neck and ears. It crops the grass going backwards, for its upper lip 
is so long that if it were to feed while going forward it would cover up 
the grass. It has its legs without any joints and so when it wishes to go 
to sleep it leans against a tree; and the hunters after having reconnoitred 
the spot at which it is accustomed to sleep saw the tree almost through, 
and when afterwards it leans against it as it sleeps it falls in its sleep and 
so the hunters take it. Every other method of capturing it is bound to 
fail because it runs with incredible speed. 

^ H 21 V. 


This is a native of Paconia, and it has a neck with a mane like a horse: 
in all other respects it resembles a bull except that its horns bend inwards 
to such an extent that it cannot butt with them. This is why its only 
refuge is in flight, in which it voids its excrement a distance of four 
hundred braccia from its course, and wherever this touches it burns like 


These keep their claws in sheath and never put them out except 
when on the back of their prey or an enemy. 


When the lioness defends her cubs from the hands of the hunters, 
in order not to be affrighted by the spears she lowers her eyes to the 
ground, so that her cubs may not be taken prisoners through her flight. 


This animal which is so terrible fears nothing more than the noise of 
empty carts and in like manner the crowing of cocks, and when it sees 
these it is much terrified, gazes at their combs with a look of fear and is 
strangely perturbed even though its face is covered. 





This has the shape of a lioness, but it is taller in the leg and slimmer 
and longer and quite white, marked with black spots after the manner of 
rosettes; all the animals are fascinated by these as they gaze at them and 
they would remain standing there always if it were not for the terror of 
its face; being conscious of this therefore it hides its face, and the animals 
that are round about it take courage and draw near so as to be able the 
better to enjoy so much beauty: it then suddenly seizes on the nearest 
and instantly devours it. , 

H 22 V. and 23 r. 


The Bactrian have two humps, the Arabian one. They are swift in 
battle and very useful for carrying burdens. This animal is a great 
observer of rule and proportion, for it does not move at all if its load is 
larger than it is accustomed to, and if it is taken too long a journey it 
does the same and stops suddenly, so that the merchants are obliged to 
make their lodging there. ^ ^ 


This is a native of Hyrcania; it bears some resemblance to the panther 
from the various spots on its skin; and it is an animal of terrifying speed. 
When the hunter finds its cubs he carries them off instantly, after placing 
mirrors at the spot from which he has taken them, and then immediately 
takes to flight upon a swift horse. 

The panther when it returns finds the mirrors fixed to the ground 
and in looking at these it thinks that it sees its own children, until by 
scratching with its paw it discovers the fraud and then following the 
scent of its cubs it pursues the hunter. And as soon as the hunter sees 
the tigress he abandons one of the cubs, and this she takes and carries it 
to her lair and instantly sets off again after the hunter, and this is repeated 
until he gains his boat. 

° H 23 V. and 24 r. 


It is found in Ethiopia near to the principal source of the Niger, 
It is an animal which is not very large. It is sluggish in all its limbs and 
has the head so large that it carries it awkwardly, in such a way that it is 

HH 2 481 


always mclined towards the ground; otherwise it would be a very great 
pest to mankind, for anyone on whom it fixes its eyes dies instantly. 

H 24 r, 


It is found in the province of Cyrenaica and is not more than twelve 
fingers long. It has a white spot on its head of the shape of a diadem. 
It drives away every serpent by its whistling. It resembles a snake but 
does not move by wriggling, but extends itself straight forward from its 
centre. It is said that on one occasion when one of these was killed by a 
horseman’s spear and its venom flowed over the spear, not only the man 
died but the horse did also. It spoils the corn, not only that which it 
touches but that upon which it breathes; it scorches the grass and splits 

stones. HHr.andy. 


This on finding the den of the basilisk kills it with the smell of its 
urin§ by spreading this about, and the smell of this urine often kills the 
weasel itself. 


These have four small movable horns; and when they wish to feed 
they hide the whole of their body except these tiny horns under the 
leaves, and as they move these it seems to the birds that they are little 
worms wriggling about, and so they instantly descend and peck at 
them. And then the ceraste immediately wraps itself round them in a 
circle and so devours them. h 24 v 


This has two heads, one in its usual place the other at its tail, as 
though it was not sufficient for it to throw its poison from one place 


This stations itself in trees and hurls itself like a dart, and transfixes 
the wild beasts and slays them. 


There is no remedy for the bite of this animal except instantly to 
cut away the part affected. Pestilential though it is this animal has so 



strong an afFeotion for its companion that they always go in pairs. And 
if by a mischance one of them should be slain the other pursues the 
murderer with incredible speed, and is so alert and eager for vengeance 
as to overcome every obstacle. It will pass through a whole troop seeking 
only to wound its enemy, traversing any distance, and the only ways of 
avoiding it are by crossing over water or by a very rapid flight. Its eyes 
turn inwards and it has large ears, and its hearing guides it more than its 

H 25 r. 


This animal is the mortal enemy of the asp. It is a native of Egypt, 
and when it sees an asp near to its place it runs instantly to the mud or 
slime of the Nile and covers itself with it entirely, and then after drying 
itself in the sun smears itself again with mud, and thus drying itself 
time after time covers itself with three or four coats like coats of mail; 
after this it attacks the asp and struggles with it determinedly, until it 
seizes its opportunity and flies at its throat and chokes it. ^ ^ ^ 


This is a native of the Nile. It has four feet and is dangerous both on 
land and in the water. It is the only land animal that is without a tongue, 
and it bites merely by moving its upper jaw. It grows to a length of 
forty feet, it has claws, and is covered with hide that will withstand any 
blow. It remains on land by day and in the water by night. 'When it 
has had its meal of fish it goes to sleep on the bank of the Nile with its 
mouth open, and then the bird called trochilus, a very small bird, runs 
immediately to its mouth, and hopping about among its teeth in and 
out proceeds to peck at the remains of its food, and causing it entrancing 
pleasure thereby tempts it to open its mouth more widely, and in so 
doing it falls asleep. No sooner does the ichneumon perceive this than 
it flings itself into its mouth, pierces its stomach and intestines, and so 
finally kills it. , , 

H 25 V. and 20 r. 


Nature has given such power of understanding to animals that in 
addition to the perception of what is to their own advantage they know 
what is to the disadvantage of the enemy; as a consequence the dolphin 
knows both the power of a cut from the fins which it has on its back, and 



the tenderness of the belly of the crocodile, hence when they fight it 
glides underneath it, pierces its belly and so kills it. 

The crocodile is terrifying to those who flee from him and an utter 
coward when he is being pursued. h 26 r 


This when it feels itself becoming overloaded looks about for thorns 
or where there are the fragments of split canes, and there it rubs a vein 
so hard as to burst it open, and then having allowed as much blood to 
flow as may be necessary it besmears itself with mud and so plasters up 
the wound. It has almost the shape of a horse, with cloven hoofs, twisted 
tail, boar’s tusks, and neck with flowing mane. The hide cannot be 
pierced except when it is bathing. It feeds on corn that grows in the 
fields, and makes its way into them backwards, so that it may appear that 
it has just emerged. 


This bears a resemblance to a stork, and when it feels ill it fills its 
crop with water and makes an injection with its beak. 


This when it feels itself bitten by the spider called phalangium eats 
crabs and rids itself of the poison. h26v 


This when it fights with serpents eats sow-thistles and gains its 


This gives sight to its blind young with the juice of the celandine. 


This when it chases rats eats first of rue. 

W I L D B O A R 

This cures its diseases by eating ivy. 


This when it wishes to renew itself casts its old slough, commencing 
by the head : it transforms itself in a day and a night. 




This will still fight with the dogs and the hunters after its entrails 
have fallen out. 

H 27 r. 


This always takes the colour of the object on which it is resting; as a 
consequence they are often devoured by the elephants together with the 
leaves on which they are resting. 


This when it has slain the chameleon purges itself with laurel. 

H 27 V. 

‘Loyalty. The cranes in order that their king 
may not perish by their keeping bad guard stand 
round him at night holding stones in their feet. 
Love, fear and reverence — write these upon the 
three stones of the crane.’ 

A man on seeing a large sword at another man’s side said to him:— 
‘Oh you poor fellow! I have been watching you now for a long time 
tied to this weapon. Why don’t you release yourself since your hands 
are free, and thus regain your liberty?’ To this the other made answer:— 
‘This is not your affair, and in any case it is an old state of things.’ 
The first feeling himself insulted said:— ‘I look on you as having a 
knowledge of so few matters in this world that I supposed that anything 
I could tell you would rank as new.’ , 

J C.A. 1 3 r. d 

Where fortune enters there envy lays siege and strives against it, 
and when this departs it leaves anguish and remorse behind. 

When fortune comes seize her with a firm hand. In front, I counsel 
you, for behind she is bald. 

J ^ C.A. 70 V. a 


Patience serves as a protection against wrongs as clothes do against 
cold. For if you put on more clothes as the cold increases it will have no 
power to hurt you. So in like manner you must grow in patience when 
you meet with great wrongs, and they will then be powerless to vex 
your mind. cA.riyv.b 

The spider, thinking to find repose within the keyhole, finds death. 

C.A. 299 V. b 

A simile. A vessel of unbaked clay when broken may be remoulded, 
but not one that has passed through the fire. ^ 

Fame should be represented in the shape of a bird, but with the 
whole figure covered with tongues instead of feathers. ^ ^ ^ 

By the cloth that is held by the hand in the current of a running 
stream, in the water of which it leaves all its impurities, is meant that . . . 

By the thorn upon which are grafted good fruits is meant that which 
is not of itself predisposed to virtue, yet by the help of an instructor 
produces the most useful virtues. 



One pushes down another: by these cubes ^ are represented the life 
and conditions of mankind. g 89 r ’ 

Envy wounds by base calumnies, that is by slander, at which virtue 
is filled with dismay. h6o[i2]v. 

Good Report soars and rises up to heaven, for virtuous things find 
favour with God. Evil Report should be shown inverted, for all her 
works are contrary to God and tend towards hell. h 61 [13] r 

The goldfinch will carry spurge to its little ones imprisoned in a 
cage: death rather than loss of liberty. h63[i5]v 

[For an allegorical refresentation\ 

II Moro with the spectacles and Envy represented with lying Slander, 
and Justice black for 11 Moro. 

Labour with the vine in her hand. ^ gg ^ 

The ermine with mud. 

Galeazzo between time of tranquillity and flight of fortune. 

The ostrich which with patience produces its young. 

Bars of gold are refined in the fire. ^ 

Magnanimity. The falcon only takes the large birds, and will die 
rather than eat flesh that has become tainted. 

Constancy. Not he who begins but he who endures. ^ loi [42 v] r 

Loyalty. The cranes in order that their king may not perish by 
their keeping bad guard stand round him at night holding stones in 
their feet. Love, fear and reverence — write these upon the three stones 
of the cranes. t 


The bee may be likened to deceit, for it has honey in its mouth 

and poison behind. . t 

^ r 49 [r] y. 

[For an allegorical representation^ 

II Moro as the figure of Fortune, with hair and robes and with hands 
1 MS. has a diagram with dice. 

hO *§ 

^Jhrarj of Christ Churchy Oxford 


held in front, and Messer Gualtieri with act of obeisance plucks him by 
the robes from below as he presents himself before him. 

Also Poverty as a hideous figure running behind a youth, whom 
II Moro covers with the skirt of his robe while he threatens the monster 
with his gilded sceptre, 1138 [90] v 

The evil that does not harm me is as the good that does not help 


The rushes which hold back the tiny blades of straw when they 
are drowning. 

[With drawing of faggot] 

To place in the hand of ingratitude: 
Wood feeds the fire that consumes it. 

MS. 2038 Bib. Nat. 34 r. 

F O R I N G R A T I T U D E 
[With drawing of man blowing out candle] 

When the sun appears which drives away the general darkness, you 
extinguish the light that drives away the particular darkness, for your 
necessity and convenience. bm 173 r 

Ivy is the [emblem] of longevity. Windsor: Drawings 

Truth the sun 

falsehood a mask 


Fire destroys falsehood, that is sophistry, and restores truth, driving 
out darkness. 

Fire is to be put for the destroyer of every sophistry and the revealer 
and demonstrator of truth, because it is light, the banisher of darkness 
which is the concealer of all essential things. 



Fire destroys all sophistry, that is deceit* and maintains truth alone, 
that is gold. 

Truth in the end cannot be concealed. 

' ' ■ ■ ■ ■ 491 


Dissimulation profits nothing. Dissimulation is frustrated before so 
great a judge. 

Falsehood assumes a mask. 

Nothing is hidden beneath the sun. 

Fire is put for truth because it destroys all sophistry and lies, and the 
mask for falsity and lying by which the truth is concealed. 

Windsor: Drawings 12700 v. 

\Sketch, Figures seated on clouds. Rain. Ground below strewn with 

On this side Adam and on that Eve. 

Oh human misery! of how many things do you make yourself the 
slave for money! Windsor: Drawings 12698 r. 

This Envy is represented making a contemptuous motion towards 
heaven, because if she could she would use her strength against God. 
She is made with a mask upon her face of fair appearance. She is made 
wounded in the eye by palm and olive. She is made wounded in the 
ear by laurel and myrtle, to signify that victory and truth offend her. 
She is made with many lightnings issuing forth from her, to denote her 
evil speaking. She is made lean and wizened because she is ever wasting 
in perpetual desire. She is made with a fiery serpent gnawing at her 
heart. She is given a quiver with tongues for arrows, because with 
the tongue she often offends; and she is made with a leopard’s skin, 
since the leopard from envy slays the lion by guile. She is given a vase 
in her hand full of flowers, and beneath these filled with scorpions and 
toads and other venomous things. She is made riding upon death, 
because envy never dying has lordship over him; and death is made with 
a bridle in his mouth and laden with various weapons, since these are all 
the instruments of death. 

In the moment when virtue is born she gives birth to envy against 
herself, and a body shall sooner exist without a shadow than virtue 
without envy. Oxford Drawings, Part ii. No. 6 

Pleasure and Pain are represented as twins, as though they were 
joined together, for there is never the one without the other; and they 
turn their backs because they are contrary to each other. 

If you shall choose pleasure, know that he has behind him one who 
will deal out to you tribulation and repentance. 


FRANCIS I AND LEO X {See Popp : Leonardo Zekbnungen) 


This is pleasure together with pain, and they are represented as 
twins because the one is never separated from the other. 

They are made with their backs turned to each other because they 
are contrary the one to the other. They are made growing out of the 
same trunk because they have one and the same foundation, for the 
foundation of pleasure is labour with pain, and the foundations of pain 
are vain^ and lascivious pleasures. 

And accordingly it is represented here with a reed in the right hand, 
which is useless and without strength, and the wounds made with it are 
poisoned. In Tuscany reeds are put to support beds, to signify that here 
occur vain dreams, and here is consumed a great part of life: here is 
squandered much useful time, namely that of the morning when the 
mind is composed and refreshed, and the body therefore is fitted to 
resume new labours. There also are taken many vain pleasures, both 
with the mind imagining impossible things, and with the body taking 
those pleasures which are often the cause of the failing of life; so that 
for this the reed is held as representing such foundations. 

Oxford Drawings, Part ii. No. 7 

^ MS., van] not varj. 


1 ^- 



‘Creatures shall be seen upon the earth who will 
always be fighting one with another with very 
great losses and frequent deaths on either side. 
These shall set no bounds to their malice . . . 
O Earth! what delays thee to open and hurl 
them headlong into the deep fissures of thy 
huge abysses and caverns, and no longer to dis- 
play in the sight of heaven so savage and ruthless 
a monster?’ 


Some poor wretch will be flattered, and these same flatterers will